{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 693,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as npl\n",
    "import scipy.linalg as spl\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = [6, 6]\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "petrol = np.array([63122, 60953, 59551, 58785, 59795, 60083, 61819, 63107, 64978,\n",
    "       66090, 66541, 67186, 67396, 67619, 69006, 70258, 71880, 73597,\n",
    "       74274, 75975, 76928, 77732, 78457, 80089, 83063, 84558, 85566,\n",
    "       86724, 86046, 84972, 88157, 89105, 90340, 91195])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "miles = np.array([[203442, 199261, 232490, 227698, 242501, 242963, 245140, 247832,\n",
    "        227899, 236491, 222819, 218390],\n",
    "       [209685, 200876, 232587, 232513, 245357, 243498, 250363, 253274,\n",
    "        226312, 241050, 230511, 229584],\n",
    "       [215215, 208237, 236070, 237226, 251746, 247868, 256392, 258666,\n",
    "        233625, 245556, 230648, 234260],\n",
    "       [218534, 203677, 236679, 239415, 253244, 252145, 262105, 260687,\n",
    "        237451, 254048, 233698, 238538],\n",
    "       [222450, 213709, 251403, 250968, 257235, 257383, 265969, 262836,\n",
    "        243515, 254496, 239796, 245029],\n",
    "       [224072, 219970, 253182, 250860, 262678, 263816, 267025, 265323,\n",
    "        242240, 251419, 243056, 245787],\n",
    "       [233302, 220730, 256645, 250665, 263393, 263805, 263442, 265229,\n",
    "        245624, 257961, 245367, 248208],\n",
    "       [233799, 219221, 259740, 252734, 267646, 265475, 267179, 271401,\n",
    "        246050, 261505, 245928, 240444],\n",
    "       [233469, 221728, 252773, 252699, 261890, 256152, 262152, 261228,\n",
    "        238701, 256402, 237009, 242326],\n",
    "       [224840, 218031, 247433, 251481, 258793, 258487, 265026, 260838,\n",
    "        242034, 252683, 237342, 239774],\n",
    "       [220177, 210968, 251858, 254014, 257401, 260159, 265861, 264358,\n",
    "        244712, 256867, 239656, 240932],\n",
    "       [222724, 213547, 250410, 249309, 254145, 258025, 260317, 260623,\n",
    "        241764, 252058, 238278, 244615],\n",
    "       [226834, 218714, 253785, 249567, 261355, 260534, 260880, 264983,\n",
    "        239001, 254170, 240734, 238876],\n",
    "       [228607, 216306, 250496, 252116, 263923, 260023, 264570, 268609,\n",
    "        242582, 259281, 240146, 241365],\n",
    "       [226444, 215166, 252089, 257947, 268075, 264868, 272335, 271018,\n",
    "        249125, 267185, 242816, 253618]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 536,
   "metadata": {},
   "outputs": [],
   "source": [
    "house_sales = {'baths': np.array([2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2,\n",
    "       2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2,\n",
    "       2, 2, 2, 2, 1, 3, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2,\n",
    "       3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 3, 2, 1, 2,\n",
    "       1, 3, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 2, 3, 4, 3, 1, 3, 3, 2, 2, 3,\n",
    "       2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 1,\n",
    "       2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1,\n",
    "       2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2,\n",
    "       1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 1,\n",
    "       2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 3, 1, 2, 2, 2, 2, 2,\n",
    "       2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2,\n",
    "       2, 1, 3, 1, 2, 2, 2, 2, 2, 3, 4, 2, 2, 3, 4, 2, 1, 2, 1, 3, 4, 3,\n",
    "       2, 3, 3, 2, 3, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,\n",
    "       1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2,\n",
    "       2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1,\n",
    "       2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2,\n",
    "       1, 2, 1, 2, 3, 2, 1, 2, 2, 2, 3, 1, 2, 2, 1, 3, 2, 1, 2, 2, 2, 2,\n",
    "       1, 3, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 1, 2, 2,\n",
    "       2, 2, 2, 3, 2, 2, 2, 1, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2,\n",
    "       3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 3, 2,\n",
    "       3, 3, 3, 2, 2, 4, 3, 2, 4, 3, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1,\n",
    "       1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2,\n",
    "       2, 2, 2, 2, 3, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
    "       2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
    "       2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2,\n",
    "       2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2,\n",
    "       3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2,\n",
    "       2, 3, 2, 3, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 3,\n",
    "       2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 2, 3, 2, 3, 3, 2, 2, 3, 3,\n",
    "       2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 1, 2, 3, 1, 3, 3, 3, 2, 3, 2,\n",
    "       1, 1, 3, 4, 3, 3, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 1,\n",
    "       1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1,\n",
    "       2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2,\n",
    "       2, 1, 2, 1, 1, 3, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 1, 2,\n",
    "       1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3,\n",
    "       2, 2, 2, 2]), 'location': np.array([2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3,\n",
    "       2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3,\n",
    "       3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 4, 2, 2, 3, 3, 2,\n",
    "       3, 3, 3, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2,\n",
    "       3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 2, 2, 3, 2, 2, 3, 2, 3, 3, 4, 3, 3,\n",
    "       3, 3, 2, 3, 3, 2, 3, 2, 1, 3, 4, 3, 3, 3, 2, 4, 3, 3, 3, 4, 2, 2,\n",
    "       1, 3, 2, 3, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 2,\n",
    "       3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 3,\n",
    "       2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 3,\n",
    "       2, 2, 3, 2, 2, 3, 3, 2, 4, 2, 3, 2, 2, 3, 2, 3, 1, 2, 2, 4, 2, 3,\n",
    "       3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 2, 4, 2, 4, 2, 2, 3, 2, 2, 3, 4, 4,\n",
    "       3, 3, 2, 1, 4, 3, 4, 3, 1, 3, 3, 4, 4, 3, 3, 2, 1, 4, 2, 3, 2, 2,\n",
    "       2, 3, 3, 2, 4, 2, 1, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2,\n",
    "       2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 4, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 2,\n",
    "       2, 3, 4, 3, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 4,\n",
    "       2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 4, 4, 2, 2, 3, 2,\n",
    "       2, 3, 2, 2, 3, 3, 2, 3, 3, 2, 1, 4, 4, 2, 3, 3, 3, 2, 3, 3, 2, 3,\n",
    "       2, 2, 3, 2, 3, 2, 3, 3, 4, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2,\n",
    "       2, 3, 4, 2, 2, 4, 2, 2, 3, 3, 3, 2, 3, 1, 2, 4, 2, 3, 3, 2, 3, 3,\n",
    "       2, 2, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 2, 2, 1, 4, 3, 1, 2, 1,\n",
    "       2, 4, 1, 4, 3, 3, 2, 4, 2, 3, 4, 4, 2, 3, 4, 2, 4, 3, 3, 2, 2, 2,\n",
    "       1, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2,\n",
    "       2, 3, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 2, 3, 3, 2, 2, 3, 3, 3,\n",
    "       3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 2, 2, 3, 2, 2, 4, 3, 2, 4, 3, 3, 3,\n",
    "       3, 2, 3, 2, 2, 4, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2,\n",
    "       2, 2, 3, 3, 4, 2, 1, 1, 2, 3, 2, 3, 3, 2, 2, 3, 3, 4, 2, 2, 3, 2,\n",
    "       2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 4, 2, 2, 4, 2, 3,\n",
    "       3, 2, 4, 3, 2, 2, 2, 3, 3, 3, 2, 2, 2, 3, 4, 3, 1, 2, 4, 3, 4, 3,\n",
    "       2, 2, 4, 4, 3, 4, 2, 4, 2, 2, 3, 2, 4, 3, 2, 2, 2, 2, 2, 2, 4, 3,\n",
    "       2, 4, 4, 3, 4, 4, 3, 3, 2, 4, 3, 4, 1, 2, 4, 1, 4, 3, 4, 2, 4, 2,\n",
    "       2, 1, 4, 3, 4, 4, 3, 3, 3, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 3,\n",
    "       2, 2, 3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 2, 1,\n",
    "       3, 2, 3, 2, 3, 3, 2, 2, 3, 1, 3, 2, 2, 4, 3, 3, 3, 2, 3, 3, 2, 3,\n",
    "       3, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 3, 2, 1, 2, 3, 2, 4,\n",
    "       2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 4, 3, 3, 3, 3,\n",
    "       3, 2, 3, 4]), 'price': np.array([ 94.905,  98.937, 100.309, 106.25 , 107.502, 108.75 , 110.7  ,\n",
    "       113.263, 116.25 , 120.   , 121.63 , 122.   , 122.682, 123.   ,\n",
    "       124.1  , 125.   , 126.64 , 127.281, 129.   , 131.2  , 132.   ,\n",
    "       133.   , 134.555, 136.5  , 138.75 , 141.   , 146.25 , 147.308,\n",
    "       148.75 , 149.593, 150.   , 152.   , 154.   , 156.896, 161.25 ,\n",
    "       161.5  , 164.   , 165.   , 166.357, 166.357, 168.   , 170.   ,\n",
    "       173.   , 174.25 , 174.313, 178.48 , 178.76 , 181.   , 181.872,\n",
    "       182.587, 182.716, 182.75 , 183.2  , 188.741, 189.   , 192.067,\n",
    "       194.   , 194.818, 198.   , 199.5  , 200.   , 200.   , 208.   ,\n",
    "       212.864, 221.   , 221.   , 223.058, 227.887, 231.477, 234.697,\n",
    "       235.   , 236.   , 236.685, 237.8  , 240.122, 242.638, 244.   ,\n",
    "       244.96 , 245.918, 250.   , 250.   , 250.134, 254.2  , 254.2  ,\n",
    "       258.   , 260.   , 260.014, 265.   , 271.742, 273.75 , 275.086,\n",
    "       280.987, 285.   , 287.417, 291.   , 292.024, 297.   , 298.   ,\n",
    "       299.   , 304.037, 311.   , 315.537, 320.   , 328.36 , 334.15 ,\n",
    "       335.75 , 335.75 , 344.25 , 346.21 , 347.029, 347.65 , 351.3  ,\n",
    "       370.5  , 372.   , 375.   , 381.3  , 381.942, 387.731, 391.   ,\n",
    "       394.47 , 395.   , 400.186, 415.   , 425.   , 430.   , 460.   ,\n",
    "       461.   , 489.332, 510.   , 539.   , 660.   ,  69.   ,  70.   ,\n",
    "        71.   ,  78.   ,  78.4  ,  80.   ,  89.   ,  90.   ,  90.   ,\n",
    "        92.   ,  93.675,  98.   ,  98.   ,  99.   , 100.   , 106.716,\n",
    "       111.   , 111.   , 114.8  , 120.108, 123.225, 123.75 , 125.   ,\n",
    "       125.   , 126.   , 129.   , 134.   , 135.   , 135.5  , 140.   ,\n",
    "       140.   , 142.5  , 143.5  , 145.   , 145.   , 145.   , 146.   ,\n",
    "       148.5  , 149.   , 150.   , 150.   , 152.   , 156.   , 156.   ,\n",
    "       156.   , 157.788, 161.653, 161.829, 165.   , 168.   , 169.   ,\n",
    "       175.   , 176.25 , 179.   , 180.   , 180.4  , 182.   , 184.5  ,\n",
    "       185.   , 189.   , 194.   , 195.   , 200.   , 205.   , 205.   ,\n",
    "       205.   , 207.   , 215.   , 215.   , 222.381, 225.   , 225.   ,\n",
    "       225.   , 228.   , 229.665, 230.   , 230.   , 230.   , 234.   ,\n",
    "       235.   , 236.25 , 245.   , 245.   , 245.   , 250.   , 250.   ,\n",
    "       250.   , 255.   , 257.729, 260.   , 261.   , 264.469, 265.   ,\n",
    "       270.   , 270.   , 275.   , 275.   , 280.   , 286.013, 292.   ,\n",
    "       292.   , 293.993, 294.   , 296.769, 300.   , 300.   , 300.5  ,\n",
    "       305.   , 319.789, 330.   , 330.   , 331.   , 334.   , 336.   ,\n",
    "       339.   , 339.   , 345.   , 356.   , 361.745, 361.948, 370.   ,\n",
    "       385.   , 399.   , 402.   , 406.026, 420.   , 425.   , 445.   ,\n",
    "       450.   , 460.   , 460.   , 465.   , 471.75 , 484.   , 495.   ,\n",
    "       572.5  , 582.   , 613.401, 680.   , 699.   ,  61.5  ,  62.05 ,\n",
    "        65.   ,  65.   ,  68.   ,  68.   ,  77.   ,  82.732,  84.   ,\n",
    "        84.675,  85.   ,  90.   ,  90.   ,  91.   ,  95.   ,  97.5  ,\n",
    "       100.   , 101.   , 102.75 , 112.5  , 113.   , 114.   , 114.   ,\n",
    "       114.75 , 115.   , 115.   , 116.1  , 119.25 , 120.   , 120.   ,\n",
    "       120.108, 121.5  , 121.725, 122.   , 123.   , 125.   , 125.573,\n",
    "       126.714, 126.96 , 127.   , 127.5  , 130.   , 133.105, 136.5  ,\n",
    "       139.5  , 140.   , 140.8  , 145.   , 147.   , 149.6  , 150.   ,\n",
    "       150.   , 155.   , 155.435, 155.5  , 158.   , 158.   , 160.   ,\n",
    "       160.   , 164.   , 164.   , 165.   , 167.   , 167.293, 167.293,\n",
    "       168.   , 170.   , 170.   , 170.   , 174.   , 178.   , 180.   ,\n",
    "       180.   , 180.   , 182.   , 188.325, 191.5  , 192.   , 192.7  ,\n",
    "       195.   , 197.654, 198.   , 200.345, 203.   , 207.   , 208.   ,\n",
    "       210.   , 212.   , 213.675, 213.697, 215.   , 215.   , 215.1  ,\n",
    "       217.5  , 218.   , 220.   , 221.   , 222.9  , 223.139, 225.5  ,\n",
    "       228.327, 230.   , 230.   , 230.522, 231.2  , 232.   , 232.5  ,\n",
    "       233.641, 234.   , 234.5  , 235.   , 236.073, 238.   , 238.861,\n",
    "       239.7  , 240.   , 240.   , 241.   , 245.   , 246.   , 247.234,\n",
    "       247.48 , 249.862, 251.   , 252.155, 254.172, 258.   , 260.   ,\n",
    "       261.   , 261.   , 262.5  , 266.   , 266.   , 270.   , 274.425,\n",
    "       275.336, 277.98 , 280.   , 284.686, 284.893, 285.   , 285.   ,\n",
    "       295.   , 296.   , 296.056, 297.359, 299.94 , 305.   , 311.328,\n",
    "       313.138, 316.63 , 320.   , 320.   , 325.   , 328.578, 331.   ,\n",
    "       340.   , 345.746, 351.   , 353.767, 356.035, 360.552, 362.305,\n",
    "       365.   , 370.   , 378.   , 388.   , 395.1  , 400.   , 408.431,\n",
    "       423.   , 427.5  , 430.922, 445.   , 450.   , 452.   , 470.   ,\n",
    "       475.   , 484.5  , 500.   , 506.688, 528.   , 579.093, 636.   ,\n",
    "       668.365, 676.2  , 691.659,  55.422,  63.   ,  65.   ,  65.   ,\n",
    "        65.   ,  66.5  ,  71.   ,  75.   ,  77.   ,  85.   ,  95.625,\n",
    "        96.14 , 104.25 , 105.   , 108.   , 109.   , 115.   , 115.   ,\n",
    "       115.5  , 115.62 , 116.   , 122.   , 122.5  , 123.   , 124.   ,\n",
    "       124.   , 124.413, 125.   , 130.   , 131.75 , 137.721, 137.76 ,\n",
    "       138.   , 140.   , 145.   , 145.   , 150.   , 150.   , 151.   ,\n",
    "       155.   , 155.8  , 156.142, 158.   , 160.   , 161.5  , 161.6  ,\n",
    "       162.   , 165.   , 165.   , 167.293, 168.   , 168.   , 168.75 ,\n",
    "       168.75 , 170.   , 170.25 , 173.   , 176.095, 176.25 , 178.   ,\n",
    "       179.   , 180.   , 180.   , 180.   , 181.   , 182.   , 182.587,\n",
    "       185.074, 185.833, 186.785, 187.   , 188.335, 190.   , 190.   ,\n",
    "       190.   , 190.   , 191.25 , 193.   , 193.5  , 195.   , 195.   ,\n",
    "       195.   , 198.   , 199.9  , 200.   , 201.   , 204.918, 205.   ,\n",
    "       205.878, 207.   , 207.744, 209.   , 210.   , 210.944, 213.75 ,\n",
    "       215.   , 215.   , 220.   , 220.   , 220.   , 220.   , 220.   ,\n",
    "       220.702, 222.   , 222.75 , 225.   , 225.   , 228.75 , 229.   ,\n",
    "       230.095, 232.5  , 233.   , 233.5  , 239.   , 240.   , 240.   ,\n",
    "       240.971, 242.   , 243.45 , 243.5  , 246.544, 246.75 , 247.   ,\n",
    "       249.   , 249.   , 250.   , 250.   , 252.   , 255.   , 255.   ,\n",
    "       255.   , 257.2  , 260.   , 260.   , 263.5  , 266.51 , 275.   ,\n",
    "       276.   , 276.5  , 278.   , 279.   , 280.   , 280.   , 285.   ,\n",
    "       288.   , 289.   , 290.   , 290.   , 293.996, 294.173, 295.   ,\n",
    "       298.   , 299.   , 300.   , 300.   , 300.   , 300.567, 303.   ,\n",
    "       305.   , 310.   , 310.   , 310.   , 311.518, 312.   , 315.   ,\n",
    "       315.   , 315.   , 315.   , 320.   , 322.   , 325.   , 328.37 ,\n",
    "       330.   , 331.2  , 332.   , 334.   , 335.   , 341.   , 346.375,\n",
    "       349.   , 350.   , 350.   , 350.   , 351.   , 360.   , 367.463,\n",
    "       380.   , 380.578, 386.222, 395.5  , 397.   , 400.   , 413.5  ,\n",
    "       415.   , 420.454, 425.   , 441.   , 445.   , 446.   , 450.   ,\n",
    "       455.   , 525.   , 545.   , 575.   , 575.   , 598.695, 600.   ,\n",
    "       610.   ,  56.95 ,  60.   ,  61.   ,  62.   ,  68.566,  70.   ,\n",
    "        80.   ,  85.5  ,  92.   ,  93.6  ,  95.   ,  97.75 , 104.   ,\n",
    "       105.   , 107.666, 109.   , 110.   , 110.   , 112.5  , 114.8  ,\n",
    "       116.   , 121.5  , 122.   , 123.675, 126.854, 127.059, 128.687,\n",
    "       129.5  , 130.   , 131.75 , 132.   , 134.   , 134.   , 142.   ,\n",
    "       143.012, 145.846, 147.   , 148.75 , 150.   , 150.454, 151.087,\n",
    "       157.296, 157.5  , 160.   , 160.   , 161.25 , 164.   , 165.   ,\n",
    "       165.75 , 166.   , 169.   , 170.   , 170.   , 170.725, 171.75 ,\n",
    "       172.   , 173.056, 174.   , 174.25 , 176.85 , 179.5  , 185.   ,\n",
    "       188.7  , 189.   , 189.   , 189.836, 190.   , 191.25 , 191.675,\n",
    "       195.5  , 198.   , 200.   , 200.   , 200.   , 201.528, 204.75 ,\n",
    "       205.   , 205.   , 205.9  , 207.   , 207.973, 208.25 , 208.318,\n",
    "       209.347, 211.5  , 212.   , 213.   , 216.   , 216.021, 219.   ,\n",
    "       219.794, 220.   , 220.   , 220.   , 223.   , 224.   , 224.252,\n",
    "       225.   , 228.   , 229.027, 229.5  , 230.   , 230.   , 232.425,\n",
    "       234.   , 235.   , 235.301, 235.738]), 'beds': np.array([2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 3, 3, 4, 4, 3, 3, 3, 3, 3, 4, 3, 2,\n",
    "       3, 3, 3, 2, 3, 3, 4, 4, 1, 2, 3, 3, 2, 4, 4, 4, 4, 4, 3, 3, 4, 3,\n",
    "       4, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 2,\n",
    "       5, 4, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 5, 3, 4, 2, 3, 4, 5, 3, 3, 3,\n",
    "       3, 4, 3, 4, 4, 4, 3, 2, 5, 3, 2, 5, 4, 5, 5, 4, 2, 3, 4, 3, 4, 3,\n",
    "       4, 4, 4, 3, 5, 5, 4, 4, 3, 4, 3, 4, 3, 5, 5, 5, 4, 4, 5, 4, 3, 2,\n",
    "       4, 2, 2, 2, 3, 4, 3, 2, 3, 2, 2, 1, 3, 1, 3, 3, 3, 2, 3, 3, 3, 3,\n",
    "       3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 4, 3, 4, 3, 3, 3, 4, 2, 3, 2, 2,\n",
    "       2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 4, 3, 4, 3, 3, 3, 3, 4, 4, 2,\n",
    "       4, 3, 3, 3, 4, 3, 4, 4, 3, 2, 3, 3, 3, 3, 3, 4, 2, 3, 4, 3, 3, 3,\n",
    "       4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 3, 3, 3, 3, 4, 4, 3, 4, 2, 3,\n",
    "       3, 2, 4, 3, 4, 4, 3, 4, 4, 5, 5, 3, 4, 4, 5, 4, 2, 4, 3, 4, 4, 5,\n",
    "       2, 4, 5, 4, 4, 5, 5, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3,\n",
    "       2, 1, 2, 4, 3, 3, 4, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 4,\n",
    "       4, 2, 2, 4, 3, 2, 2, 3, 3, 3, 3, 4, 3, 5, 3, 3, 3, 3, 4, 3, 3, 2,\n",
    "       2, 3, 2, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3,\n",
    "       3, 3, 2, 4, 4, 4, 3, 4, 2, 4, 4, 3, 3, 3, 2, 4, 3, 3, 4, 3, 4, 3,\n",
    "       2, 4, 3, 2, 3, 3, 2, 4, 3, 3, 4, 4, 4, 5, 4, 3, 4, 4, 4, 3, 3, 4,\n",
    "       3, 4, 2, 4, 4, 4, 4, 3, 3, 4, 3, 4, 4, 3, 3, 3, 4, 5, 4, 4, 3, 4,\n",
    "       4, 4, 3, 3, 5, 5, 5, 4, 3, 4, 3, 4, 4, 4, 4, 3, 3, 2, 3, 3, 5, 3,\n",
    "       4, 4, 2, 3, 4, 4, 5, 3, 4, 3, 3, 3, 4, 5, 4, 4, 5, 5, 2, 2, 2, 2,\n",
    "       2, 2, 2, 2, 2, 2, 3, 2, 2, 4, 2, 4, 2, 1, 3, 3, 3, 3, 3, 4, 3, 4,\n",
    "       3, 4, 3, 2, 4, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 4,\n",
    "       3, 3, 5, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 4,\n",
    "       3, 3, 3, 3, 4, 2, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3,\n",
    "       3, 1, 4, 3, 4, 4, 2, 2, 4, 3, 2, 3, 5, 3, 4, 4, 3, 3, 5, 3, 4, 3,\n",
    "       4, 4, 3, 2, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3,\n",
    "       3, 5, 3, 4, 5, 3, 4, 3, 3, 4, 3, 4, 4, 4, 4, 4, 2, 2, 3, 6, 3, 5,\n",
    "       3, 3, 3, 4, 4, 5, 4, 4, 5, 3, 3, 4, 4, 3, 4, 4, 4, 3, 3, 4, 5, 5,\n",
    "       3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 5, 4, 2, 3, 4, 3, 5, 5, 4, 4, 4, 3,\n",
    "       3, 2, 4, 5, 4, 5, 4, 1, 2, 2, 2, 2, 4, 3, 2, 2, 3, 3, 3, 3, 1, 3,\n",
    "       3, 3, 3, 3, 3, 4, 3, 2, 4, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 2, 3,\n",
    "       4, 2, 3, 3, 3, 3, 3, 4, 3, 2, 4, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 4,\n",
    "       4, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 2, 3, 2, 2, 3,\n",
    "       3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 4, 4, 3, 4,\n",
    "       3, 3, 4, 3]), 'area': np.array([0.941, 1.146, 0.909, 1.289, 1.02 , 1.022, 1.134, 0.844, 0.795,\n",
    "       0.588, 1.356, 1.118, 1.329, 1.24 , 1.601, 0.901, 1.088, 0.963,\n",
    "       1.119, 1.38 , 1.248, 1.039, 1.152, 1.38 , 1.116, 1.039, 1.418,\n",
    "       1.082, 1.472, 1.146, 0.76 , 1.304, 1.207, 1.056, 1.043, 1.587,\n",
    "       1.12 , 1.58 , 1.955, 1.656, 1.477, 1.188, 1.59 , 1.463, 1.714,\n",
    "       1.185, 1.406, 1.172, 1.152, 1.851, 1.215, 1.13 , 1.603, 1.479,\n",
    "       1.42 , 1.28 , 1.586, 1.362, 1.266, 1.715, 1.82 , 0.936, 1.511,\n",
    "       1.59 , 1.596, 1.341, 2.136, 1.616, 1.478, 1.287, 1.277, 1.448,\n",
    "       2.235, 2.093, 1.193, 2.163, 1.269, 0.958, 2.508, 1.305, 1.591,\n",
    "       1.326, 1.843, 1.921, 2.79 , 1.541, 1.018, 1.672, 0.975, 2.372,\n",
    "       1.446, 3.009, 2.056, 1.993, 1.857, 1.126, 2.494, 1.843, 1.52 ,\n",
    "       2.8  , 2.309, 2.367, 3.516, 1.914, 1.69 , 2.725, 2.354, 2.185,\n",
    "       1.801, 1.961, 3.134, 1.915, 2.734, 2.11 , 3.164, 3.599, 2.054,\n",
    "       1.83 , 1.627, 3.44 , 2.846, 2.359, 2.052, 3.433, 3.615, 2.687,\n",
    "       2.724, 3.44 , 3.508, 2.462, 2.325, 0.795, 1.099, 0.84 , 0.8  ,\n",
    "       0.746, 1.067, 1.316, 1.337, 0.868, 0.924, 0.61 , 1.22 , 0.722,\n",
    "       1.643, 0.722, 1.08 , 1.039, 1.051, 0.967, 1.098, 1.05 , 1.11 ,\n",
    "       0.888, 1.12 , 1.08 , 0.957, 0.952, 1.211, 1.264, 1.08 , 1.266,\n",
    "       0.994, 1.202, 0.722, 1.448, 1.188, 1.183, 1.32 , 1.117, 1.364,\n",
    "       1.31 , 1.006, 1.104, 0.81 , 1.123, 0.904, 1.156, 1.321, 1.392,\n",
    "       1.439, 1.159, 1.671, 1.74 , 1.265, 1.007, 1.716, 1.685, 1.829,\n",
    "       1.555, 1.12 , 1.137, 1.174, 1.393, 1.289, 1.799, 1.953, 0.723,\n",
    "       1.578, 1.317, 1.36 , 1.522, 1.751, 1.465, 1.605, 1.475, 1.216,\n",
    "       1.315, 1.567, 1.776, 2.187, 1.291, 1.503, 2.491, 1.269, 1.176,\n",
    "       1.456, 1.498, 1.574, 2.17 , 1.595, 1.567, 1.253, 1.768, 2.03 ,\n",
    "       1.531, 1.653, 2.056, 2.494, 1.45 , 2.169, 1.44 , 1.527, 1.401,\n",
    "       1.411, 1.284, 2.307, 1.91 , 1.981, 2.205, 1.449, 1.258, 2.575,\n",
    "       0.539, 2.208, 1.108, 1.595, 2.159, 1.838, 1.9  , 1.718, 3.389,\n",
    "       3.26 , 2.016, 2.607, 2.724, 3.746, 3.192, 1.247, 2.581, 2.068,\n",
    "       3.992, 3.397, 3.881, 1.598, 3.07 , 3.984, 2.222, 3.838, 2.846,\n",
    "       2.484, 0.97 , 0.623, 0.932, 0.796, 0.834, 0.834, 0.924, 0.795,\n",
    "       1.25 , 0.984, 1.013, 1.012, 0.795, 0.918, 1.082, 0.964, 0.625,\n",
    "       0.888, 1.12 , 1.331, 1.014, 1.448, 0.966, 0.779, 0.836, 1.1  ,\n",
    "       1.174, 1.207, 0.804, 0.958, 1.366, 0.901, 0.696, 1.08 , 1.104,\n",
    "       0.972, 1.39 , 1.354, 0.795, 0.78 , 1.587, 1.209, 1.139, 1.69 ,\n",
    "       1.245, 1.416, 1.3  , 1.12 , 1.59 , 1.407, 1.516, 1.646, 1.676,\n",
    "       1.37 , 1.37 , 1.351, 1.152, 1.452, 0.99 , 1.162, 1.182, 1.112,\n",
    "       1.1  , 1.28 , 1.28 , 1.039, 1.159, 1.917, 1.52 , 1.204, 1.12 ,\n",
    "       1.436, 1.451, 1.638, 1.   , 1.152, 1.154, 1.353, 1.329, 1.356,\n",
    "       1.505, 1.009, 1.144, 0.93 , 1.766, 1.94 , 1.776, 1.258, 1.872,\n",
    "       1.112, 1.856, 1.939, 0.998, 1.758, 2.142, 0.95 , 1.739, 1.516,\n",
    "       0.988, 1.555, 1.212, 1.871, 1.302, 0.756, 2.026, 1.375, 1.25 ,\n",
    "       1.058, 1.187, 1.324, 1.936, 1.427, 1.678, 1.798, 2.652, 1.816,\n",
    "       3.076, 1.844, 1.306, 2.447, 1.176, 1.182, 1.16 , 1.424, 1.574,\n",
    "       1.83 , 1.724, 1.255, 2.175, 1.904, 1.808, 2.711, 1.713, 1.457,\n",
    "       2.724, 1.468, 2.55 , 1.928, 1.922, 1.343, 1.51 , 1.559, 2.992,\n",
    "       2.109, 1.524, 1.248, 1.876, 1.851, 2.218, 1.394, 1.41 , 3.468,\n",
    "       2.346, 2.347, 1.659, 2.442, 2.155, 1.81 , 2.789, 1.606, 2.166,\n",
    "       1.871, 1.8  , 1.683, 1.596, 1.179, 1.639, 3.281, 1.697, 2.085,\n",
    "       1.939, 1.788, 1.691, 2.002, 4.303, 4.246, 2.274, 3.056, 2.503,\n",
    "       1.905, 1.32 , 3.037, 3.741, 2.66 , 3.357, 2.896, 3.788, 0.838,\n",
    "       0.904, 1.032, 0.904, 1.08 , 0.99 , 0.9  , 0.861, 0.906, 1.011,\n",
    "       1.089, 0.832, 0.8  , 1.292, 0.81 , 1.064, 0.911, 0.846, 1.32 ,\n",
    "       1.41 , 1.115, 1.169, 1.164, 1.341, 1.219, 1.127, 1.272, 1.253,\n",
    "       1.12 , 1.118, 1.89 , 1.26 , 1.4  , 1.264, 1.06 , 1.132, 1.466,\n",
    "       1.092, 1.628, 0.96 , 1.075, 1.428, 1.358, 1.41 , 1.711, 1.483,\n",
    "       1.14 , 1.549, 1.41 , 1.24 , 1.712, 1.58 , 1.669, 1.029, 1.103,\n",
    "       2.161, 1.65 , 1.2  , 1.17 , 1.199, 1.695, 1.157, 1.41 , 1.174,\n",
    "       1.593, 1.093, 1.77 , 1.436, 1.124, 1.139, 1.638, 1.328, 1.273,\n",
    "       1.082, 1.578, 0.796, 1.386, 1.452, 1.513, 1.578, 1.736, 1.473,\n",
    "       1.15 , 1.127, 1.144, 0.972, 2.306, 1.479, 1.43 , 1.8  , 1.953,\n",
    "       1.12 , 1.232, 0.984, 2.329, 1.351, 1.376, 1.566, 1.115, 1.032,\n",
    "       1.419, 1.261, 1.637, 1.338, 2.254, 1.441, 1.991, 2.126, 1.094,\n",
    "       1.462, 2.258, 1.074, 2.111, 1.686, 1.915, 2.367, 1.962, 1.406,\n",
    "       1.789, 1.876, 1.235, 2.504, 1.676, 1.367, 1.899, 1.636, 1.828,\n",
    "       1.438, 1.451, 1.52 , 1.506, 2.605, 1.196, 1.621, 1.811, 1.54 ,\n",
    "       1.543, 2.494, 1.65 , 2.214, 2.28 , 1.443, 1.582, 1.857, 1.735,\n",
    "       2.096, 1.72 , 2.16 , 1.382, 1.721, 1.328, 1.982, 1.144, 1.623,\n",
    "       1.457, 2.555, 1.577, 2.592, 1.401, 1.502, 1.327, 1.8  , 2.169,\n",
    "       2.457, 2.004, 2.212, 3.134, 1.36 , 1.276, 2.962, 1.888, 1.548,\n",
    "       2.109, 2.484, 2.258, 2.212, 1.616, 2.372, 2.606, 2.877, 2.96 ,\n",
    "       2.172, 2.1  , 1.795, 2.295, 2.577, 1.727, 1.485, 1.655, 2.049,\n",
    "       2.875, 2.199, 1.304, 2.334, 2.278, 1.493, 2.787, 2.824, 3.261,\n",
    "       2.053, 2.379, 3.173, 1.348, 1.252, 3.229, 3.863, 2.356, 3.579,\n",
    "       1.512, 0.611, 0.876, 0.933, 0.864, 1.011, 1.158, 1.092, 0.956,\n",
    "       1.139, 1.058, 1.04 , 1.354, 1.051, 0.682, 1.161, 1.004, 1.229,\n",
    "       1.249, 1.161, 1.01 , 1.462, 1.269, 1.188, 1.57 , 1.093, 0.962,\n",
    "       1.089, 1.127, 1.309, 0.97 , 1.144, 1.   , 1.206, 1.285, 1.543,\n",
    "       0.884, 1.019, 1.392, 0.924, 1.217, 1.67 , 1.302, 1.488, 1.373,\n",
    "       1.381, 1.265, 0.881, 1.608, 1.344, 1.202, 1.104, 1.232, 1.638,\n",
    "       1.177, 1.582, 0.904, 1.34 , 1.204, 1.477, 1.497, 0.96 , 1.428,\n",
    "       1.039, 1.529, 1.892, 1.887, 1.294, 1.638, 1.677, 1.073, 1.231,\n",
    "       1.175, 1.416, 1.358, 1.609, 1.968, 1.089, 1.296, 1.189, 0.795,\n",
    "       1.371, 1.31 , 1.262, 1.74 , 1.517, 1.45 , 1.416, 0.888, 1.882,\n",
    "       1.302, 1.418, 1.319, 1.77 , 1.627, 1.04 , 0.96 , 1.456, 1.45 ,\n",
    "       1.358, 1.329, 1.715, 1.262, 2.28 , 1.477, 1.216, 1.685, 1.362]), 'condo': np.array([1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,\n",
    "       0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,\n",
    "       0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0,\n",
    "       0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0])}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 556,
   "metadata": {},
   "outputs": [],
   "source": [
    "temps = np.array([59. , 57.9, 57. , 57. , 55.9, 57. , 57. , 60.1, 62.1, 64. , 64.9,\n",
    "       66. , 69.1, 68. , 69.1, 66. , 64. , 62.1, 60.1, 59. , 57.9, 57.9,\n",
    "       59. , 57.9, 57.9, 57.9, 57. , 57. , 57. , 57.9, 57.9, 59. , 61. ,\n",
    "       62.1, 64. , 64. , 64. , 64.9, 64.9, 64.9, 64. , 62.1, 61. , 59. ,\n",
    "       59. , 59. , 59. , 59. , 59. , 59. , 57.9, 57.9, 57.9, 57. , 59. ,\n",
    "       62.1, 64. , 64.9, 66. , 66.9, 66.9, 66. , 68. , 66.9, 64. , 61. ,\n",
    "       60.1, 59. , 57.9, 57. , 57.9, 57.9, 57. , 57. , 57. , 57. , 57.9,\n",
    "       57.9, 57.9, 59. , 59. , 57.9, 59. , 62.1, 64. , 64. , 64. , 64. ,\n",
    "       63. , 61. , 61. , 60.1, 60.1, 60.1, 60.1, 60.1, 60.1, 59. , 59. ,\n",
    "       59. , 60.1, 60.1, 60.1, 60.1, 61. , 63. , 63. , 63. , 64.9, 66. ,\n",
    "       68. , 66.9, 66.9, 64. , 63. , 62.1, 62.1, 60.1, 60.1, 59. , 57.9,\n",
    "       57.9, 59. , 59. , 57.9, 57.9, 59. , 60.1, 60.1, 61. , 63. , 64.9,\n",
    "       64.9, 66. , 66.9, 66.9, 64.9, 64. , 62.1, 60.1, 60.1, 60.1, 60.1,\n",
    "       59. , 59. , 60.1, 59. , 59. , 59. , 59. , 57. , 57.9, 59. , 60.1,\n",
    "       59. , 64. , 66. , 66. , 66. , 64.9, 64.9, 64. , 62.1, 61. , 61. ,\n",
    "       60.1, 60.1, 60.1, 60.1, 59. , 59. , 57.9, 57.9, 57.9, 57.9, 59. ,\n",
    "       61. , 63. , 64. , 64.9, 66. , 66. , 64.9, 64.9, 64. , 63. , 62.1,\n",
    "       61. , 61. , 60.1, 60.1, 60.1, 59. , 60.1, 59. , 59. , 57.9, 57.9,\n",
    "       59. , 60.1, 61. , 61. , 62.1, 63. , 64. , 64.9, 64. , 64.9, 64. ,\n",
    "       63. , 61. , 60.1, 59. , 59. , 59. , 59. , 59. , 59. , 57.9, 57.9,\n",
    "       59. , 59. , 60.1, 60.1, 61. , 62.1, 63. , 64. , 64.9, 66.9, 66.9,\n",
    "       66.9, 64.9, 63. , 62.1, 61. , 60.1, 60.1, 60.1, 60.1, 60.1, 60.1,\n",
    "       59. , 60.1, 59. , 60.1, 60.1, 61. , 61. , 62.1, 63. , 64.9, 66.9,\n",
    "       66.9, 66. , 64.9, 63. , 62.1, 61. , 61. , 60.1, 59. , 59. , 57.9,\n",
    "       57.9, 57.9, 57. , 57.9, 57.9, 57.9, 57.9, 59. , 61. , 64. , 64. ,\n",
    "       64. , 64.9, 64.9, 64.9, 64. , 62.1, 61. , 61. , 60.1, 60.1, 60.1,\n",
    "       60.1, 60.1, 59. , 59. , 60.1, 60.1, 60.1, 60.1, 60.1, 61. , 62.1,\n",
    "       62.1, 63. , 64. , 69.1, 68. , 68. , 66. , 64.9, 63. , 63. , 62.1,\n",
    "       62.1, 62.1, 62.1, 61. , 63. , 62.1, 61. , 61. , 61. , 61. , 61. ,\n",
    "       62.1, 62.1, 64.9, 64.9, 64.9, 66.9, 66.9, 66. , 66. , 64.9, 64. ,\n",
    "       62.1, 61. , 61. , 61. , 61. , 62.1, 63. , 62.1, 62.1, 62.1, 62.1,\n",
    "       62.1, 62.1, 62.1, 63. , 64. , 66. , 68. , 70. , 69.1, 68. , 66.9,\n",
    "       66.9, 64.9, 64. , 62.1, 61. , 61. , 61. , 61. , 61. , 62.1, 62.1,\n",
    "       62.1, 61. , 62.1, 62.1, 63. , 63. , 63. , 64.9, 66.9, 68. , 68. ,\n",
    "       68. , 68. , 66.9, 64.9, 64. , 62.1, 63. , 62.1, 62.1, 62.1, 62.1,\n",
    "       61. , 61. , 61. , 61. , 61. , 62.1, 62.1, 64. , 64. , 66. , 66.9,\n",
    "       66.9, 68. , 68. , 66.9, 66. , 64.9, 63. , 62.1, 62.1, 62.1, 61. ,\n",
    "       61. , 62.1, 61. , 61. , 61. , 61. , 61. , 61. , 61. , 61. , 62.1,\n",
    "       62.1, 63. , 63. , 62.1, 63. , 62.1, 62.1, 61. , 61. , 61. , 61. ,\n",
    "       61. , 61. , 61. , 61. , 62.1, 61. , 61. , 61. , 61. , 61. , 62.1,\n",
    "       62.1, 63. , 64. , 64.9, 64.9, 66.9, 66.9, 66.9, 64.9, 63. , 62.1,\n",
    "       61. , 61. , 61. , 61. , 60.1, 60.1, 60.1, 60.1, 59. , 57.9, 59. ,\n",
    "       59. , 61. , 62.1, 66. , 64. , 64. , 64. , 64.9, 64.9, 62.1, 63. ,\n",
    "       61. , 61. , 59. , 59. , 57.9, 57.9, 57.9, 57. , 57. , 55.9, 57. ,\n",
    "       57. , 55.9, 57. , 60.1, 62.1, 62.1, 64. , 64. , 64.9, 64. , 64. ,\n",
    "       63. , 63. , 62.1, 61. , 60.1, 60.1, 60.1, 59. , 59. , 57.9, 57.9,\n",
    "       57. , 54. , 55. , 54. , 57. , 59. , 61. , 64.9, 66. , 66.9, 66.9,\n",
    "       66. , 66. , 66. , 64.9, 64. , 64. , 61. , 61. , 60.1, 60.1, 59. ,\n",
    "       57.9, 57. , 57.9, 57. , 55.9, 57. , 57.9, 61. , 63. , 64. , 66.9,\n",
    "       69.1, 70. , 70. , 70. , 66. , 66. , 63. , 62.1, 60.1, 59. , 59. ,\n",
    "       57.9, 57.9, 57.9, 57.9, 57.9, 57.9, 57.9, 57.9, 59. , 62.1, 62.1,\n",
    "       63. , 64. , 66. , 66. , 64.9, 64.9, 64.9, 64.9, 63. , 61. , 61. ,\n",
    "       60.1, 60.1, 60.1, 59. , 57.9, 57.9, 57.9, 57. , 57. , 57. , 57.9,\n",
    "       60.1, 61. , 62.1, 63. , 64. , 64. , 64. , 64. , 66. , 64.9, 64. ,\n",
    "       62.1, 60.1, 60.1, 59. , 57.9, 57.9, 57.9, 57.9, 57.9, 55.9, 55.9,\n",
    "       57. , 59. , 61. , 63. , 64. , 66. , 66. , 68. , 68. , 66.9, 64.9,\n",
    "       64. , 63. , 63. , 61. , 60.1, 60.1, 60.1, 60.1, 59. , 59. , 59. ,\n",
    "       59. , 57.9, 57.9, 60.1, 61. , 63. , 62.1, 64.9, 66. , 66.9, 68. ,\n",
    "       68. , 66.9, 66. , 64. , 61. , 61. , 60.1, 60.1, 60.1, 60.1, 60.1,\n",
    "       61. , 61. , 60.1, 60.1, 60.1, 60.1, 61. , 62.1, 63. , 63. , 64. ,\n",
    "       66. , 66.9, 66. , 64. , 63. , 62.1, 61. , 60.1, 59. , 59. , 59. ,\n",
    "       60.1, 60.1, 60.1, 60.1, 60.1, 60.1, 59. , 60.1, 61. , 62.1, 64.9,\n",
    "       64.9, 66. , 66.9, 66.9, 66. , 66. , 66. , 64. , 62.1, 61. , 60.1,\n",
    "       60.1, 60.1, 59. , 59. , 59. , 57.9, 57.9, 59. , 60.1, 60.1, 61. ,\n",
    "       63. , 63. , 64. , 64.9, 66.9, 68. , 66. , 66. , 64.9, 63. , 62.1,\n",
    "       61. , 60.1, 61. , 60.1, 59. , 59. , 59. , 59. , 59. , 60.1, 60.1,\n",
    "       61. , 61. , 62.1, 63. , 63. , 64.9, 68. , 68. , 68. , 66. , 64.9,\n",
    "       63. , 62.1, 62.1, 62.1, 62.1, 62.1, 63. ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13.1 Least Squares Data Fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 694,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:4: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1334355c0>"
      ]
     },
     "execution_count": 694,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1333ccd30>]"
      ]
     },
     "execution_count": 694,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#petrol consumption per year via straight-line fit\n",
    "n = len(petrol)\n",
    "A = np.matrix([np.ones(n), np.array(list(range(1,n+1)))]).transpose()\n",
    "x = npl.lstsq(A,petrol)[0]\n",
    "plt.scatter(range(1980,2014),petrol)\n",
    "plt.plot(range(1980,2014), np.matmul(A,x).transpose())\n",
    "# A #list of points\n",
    "# x #least squares values\n",
    "# np.matmul(A,x).transpose() #coordinates per value in col shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 695,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:5: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  \"\"\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1335a1a20>"
      ]
     },
     "execution_count": 695,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13344bf60>]"
      ]
     },
     "execution_count": 695,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#miles traveled per month via periodic component to a time series\n",
    "m = np.shape(miles)[0]*np.shape(miles)[1]\n",
    "A = np.hstack((np.vstack(np.arange(0,m)),np.vstack([np.eye(12) for i in range(15)])))\n",
    "b = np.vstack(np.ravel(miles))#reshape(vmt',m,1)\n",
    "x = npl.lstsq(A,b)[0]\n",
    "plt.scatter(range(m),b)\n",
    "plt.plot(range(m),np.matmul(A,x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 686,
   "metadata": {},
   "outputs": [],
   "source": [
    "#polynomial fitting\n",
    "size = 100\n",
    "t = -1 + 2*np.random.rand(size,1)\n",
    "y = t**3 - t + .4 / (1 + 25*t**2) + .1*np.random.randn(size,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 687,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:1: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "polyfit = lambda x,y,z: npl.lstsq(np.vander(x,z),y)[0]\n",
    "theta2 = polyfit(np.hstack(t),y,3)\n",
    "theta6 = polyfit(np.hstack(t),y,7)\n",
    "theta10 = polyfit(np.hstack(t),y,11)\n",
    "theta15= polyfit(np.hstack(t),y,16)\n",
    "polyeval = lambda theta,x: np.matmul(np.vander(x,len(theta)),theta)\n",
    "t_plot = np.linspace(-1,1,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 690,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x132d27da0>"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x132e4ea58>"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x132e171d0>]"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x132e59278>"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x132e4ef60>]"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x132e599e8>"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x132e59748>]"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x132e59d30>"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x132e4ed30>]"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(t,y)\n",
    "fig, ax = plt.subplots(2, 2, figsize=(15,15))\n",
    "ax[0, 0].scatter(t,y)\n",
    "ax[0, 0].plot(t_plot,polyeval(theta2,t_plot), 'r') \n",
    "ax[1, 0].scatter(t,y)\n",
    "ax[1, 0].plot(t_plot,polyeval(theta6,t_plot), 'b') \n",
    "ax[0, 1].scatter(t,y)\n",
    "ax[0, 1].plot(t_plot,polyeval(theta10,t_plot), 'g') \n",
    "ax[1, 1].scatter(t,y)\n",
    "ax[1, 1].plot(t_plot,polyeval(theta15,t_plot), 'k') \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 696,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:12: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x13363db70>"
      ]
     },
     "execution_count": 696,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x133435550>]"
      ]
     },
     "execution_count": 696,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#piecewise\n",
    "size = 100\n",
    "x = -2 + (4*np.random.rand(size,1))\n",
    "y = 1 + 2*(x-1) - 3 * np.vstack([max(i+1,0) for i in x]) + 4 * np.vstack([max(i-1, 0) for i in x]) + (.3*np.random.randn(size,1))\n",
    "\n",
    "A = np.hstack((\n",
    "    np.vstack(np.ones(size)), \n",
    "     x, \n",
    "     np.vstack([max(i+1,0) for i in np.hstack(x)]), \n",
    "     np.vstack([max(i-1,0) for i in np.hstack(x)])))\n",
    "\n",
    "theta = npl.lstsq(A,y)[0]\n",
    "t = np.array([-2.1,-1,1,2.1])\n",
    "yhat = np.vstack(theta[0] + theta[1]*t) + np.vstack(theta[2]*np.vstack([max(i+1,0) for i in np.hstack(t)]) + theta[3]*np.vstack([max(i-1,0) for i in np.hstack(t)]))\n",
    "plt.scatter(x,y)\n",
    "plt.plot(t,yhat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 569,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  import sys\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 54.4016736 , 148.7250726 , -18.85335788])"
      ]
     },
     "execution_count": 569,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "74.84571649590146"
      ]
     },
     "execution_count": 569,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "112.78216159756509"
      ]
     },
     "execution_count": 569,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# house price regression\n",
    "area = house_sales[\"area\"]\n",
    "beds = house_sales[\"beds\"]\n",
    "price = house_sales[\"price\"]\n",
    "m = len(price)\n",
    "A = np.hstack([np.vstack(np.ones(m)),np.vstack(area),np.vstack(beds)])\n",
    "x = npl.lstsq(A,price)[0]\n",
    "rmse = np.sqrt(np.mean(np.square(price - np.matmul(A,x))))\n",
    "price_std = np.std(price)\n",
    "x\n",
    "rmse\n",
    "price_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 707,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0505592856293298"
      ]
     },
     "execution_count": 707,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.160243163820612"
      ]
     },
     "execution_count": 707,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.7338941400468746"
      ]
     },
     "execution_count": 707,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.0129632612687511"
      ]
     },
     "execution_count": 707,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x133b3cda0>"
      ]
     },
     "execution_count": 707,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x133f4b048>]"
      ]
     },
     "execution_count": 707,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rms = lambda x: np.sqrt(np.mean(np.square(x)))\n",
    "#auto-regressive temperature time series \n",
    "N = len(temps)\n",
    "np.std(temps)\n",
    "rms(temps[1:] - temps[0:len(temps)-1])\n",
    "rms(temps[24:] - temps[0:len(temps)-24])\n",
    "M = 8\n",
    "y = temps[M:]\n",
    "A = np.array([temps[i-1:i+N-M-1] for i in range(M,0,-1)]).transpose()\n",
    "theta = npl.lstsq(A,y)[0]\n",
    "ypred = np.matmul(A,theta)\n",
    "rms(ypred-y)\n",
    "Nplot = 24*5\n",
    "plt.scatter(range(Nplot),temps[:Nplot])\n",
    "plt.plot(range(M,Nplot),ypred[:Nplot-M],'g')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13.2 Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 785,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:14: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "#Polynomial Approximation\n",
    "#recall:\n",
    "size = 100\n",
    "t = -1 + 2*np.random.rand(size,1)\n",
    "y = t**3 - t + .4 / (1 + 25*t**2) + .1*np.random.randn(size,1)\n",
    "\n",
    "m = 100\n",
    "t_test = -1 + 2*np.random.rand(m,1)\n",
    "y_test = t_test**3 - t_test + .4 / (1+25*t_test**2)+.1*np.random.randn(m,1)\n",
    "error_train = np.zeros(21)\n",
    "error_test = np.zeros(21)\n",
    "for p in range(21):\n",
    "    A = np.vander(np.hstack(t),p)\n",
    "    theta = npl.lstsq(A,y)[0]\n",
    "    error_train[p] = npl.norm(np.matmul(A,theta)-y)/npl.norm(y)\n",
    "    error_test[p] = npl.norm(np.matmul(np.vander(np.hstack(t_test),p), theta) - y_test) / npl.norm(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 790,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x134404be0>]"
      ]
     },
     "execution_count": 790,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x134330a58>]"
      ]
     },
     "execution_count": 790,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(21),error_train, marker= \"v\")\n",
    "plt.plot(range(21),error_test, marker = '8')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1117,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:19: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 56.47245454, 149.60196824, -20.24901986],\n",
       "       [ 56.47245454, 149.60196824, -20.24901986],\n",
       "       [ 56.47245454, 149.60196824, -20.24901986],\n",
       "       [ 56.47245454, 149.60196824, -20.24901986],\n",
       "       [ 56.47245454, 149.60196824, -20.24901986]])"
      ]
     },
     "execution_count": 1117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(75.43428565493146, 72.83869258042249)"
      ]
     },
     "execution_count": 1117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#house price regression\n",
    "rms = lambda x: np.sqrt(np.mean(np.square(x)))\n",
    "N = len(price)\n",
    "X = np.hstack((np.vstack(np.ones(N)),np.vstack(area),np.vstack(beds)))\n",
    "nfold = int(N/5)\n",
    "I = np.random.permutation(N)\n",
    "coeff,error = np.zeros((5,3)), np.zeros((5,2))\n",
    "for k in range(1,6):\n",
    "    if k == 1:\n",
    "        Itrain = I[nfold+1:]\n",
    "        Itest = I[:nfold]\n",
    "    elif k==5:\n",
    "        Itrain = I[:4*nfold]\n",
    "        Itest = I[4*nfold+1:]\n",
    "    else: \n",
    "        Itrain = np.vstack((np.vstack(I[:(k-1) * nfold]), np.vstack(I[k*nfold+1:N])))\n",
    "        Itest = np.vstack((I[(k-1)*nfold+1], I[k*nfold]))\n",
    "for k in range(1,6):\n",
    "    theta = npl.lstsq(X[Itrain,:], price[Itrain])[0]\n",
    "    coeff[k-1,:] = theta\n",
    "    rms_train = rms(np.matmul(X[Itrain,:] ,theta) - price[Itrain])\n",
    "    rms_test = rms(np.matmul(X[Itest,:] ,theta) - price[Itest])\n",
    "\n",
    "coeff\n",
    "rms_train, rms_test\n",
    "\n",
    "##BUGGY IMPLEMENTATION, FOR LOOP SEQUENCE NOT APPENDING MATRIX ITEMS CORRECTLY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1070,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:13: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  del sys.path[0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2.920374350997982e-14"
      ]
     },
     "execution_count": 1070,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "4.17119944655552"
      ]
     },
     "execution_count": 1070,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1351f63c8>"
      ]
     },
     "execution_count": 1070,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1351e3ba8>]"
      ]
     },
     "execution_count": 1070,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#recall temps:\n",
    "N = len(temps)\n",
    "M = 8\n",
    "# A = np.array([temps[i-1:i+N-M-1] for i in range(M,0,-1)]).transpose()\n",
    "\n",
    "Ntrain = 24*24\n",
    "t_train = temps[1:Ntrain]\n",
    "Ntest = N-Ntrain\n",
    "t_test = temps[Ntrain+1:]\n",
    "m = Ntrain-M\n",
    "y = t_train[M-1:M+m]\n",
    "A = np.array(np.hstack([np.vstack(t_train[i-1:i+m-1]) for i in range(M,0,-1)]))#.transpose()\n",
    "coeff = npl.lstsq(A,y)[0]\n",
    "rms_train = rms(np.matmul(A,coeff)-y)\n",
    "rms_train\n",
    "ytest = t_test[M+1:]\n",
    "mtest = len(ytest)\n",
    "ypred = np.matmul(np.array(np.hstack([np.vstack(t_test[i-1:i+mtest-1]) for i in range(M,0,-1)])), coeff)#.transpose()\n",
    "rms_test = rms(ypred - np.vstack(ytest))\n",
    "rms_test\n",
    "Nplot = 24*5\n",
    "plt.scatter(range(Nplot), t_test[:Nplot])\n",
    "plt.plot(range(M,Nplot), ypred[:Nplot-M], 'orange')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13.3 Feature Engineering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1095,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:12: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "68.34428699036884"
      ]
     },
     "execution_count": 1095,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "price,area,beds,condo,location = house_sales[\"price\"],house_sales[\"area\"],house_sales[\"beds\"],house_sales[\"condo\"],house_sales[\"location\"]\n",
    "N = len(price)\n",
    "a = np.vstack(np.ones(N))\n",
    "b = np.vstack(area)\n",
    "c = np.vstack([max(i-1.5,0) for i in np.hstack(area)])\n",
    "d = np.vstack(beds)\n",
    "e = np.vstack(condo)\n",
    "f = np.vstack(location == 2).astype(int)\n",
    "g = np.vstack(location == 3).astype(int)\n",
    "h = np.vstack(location == 4).astype(int)\n",
    "X = np.hstack((a,b,c,d,e,f,g,h))\n",
    "theta = npl.lstsq(X,price)[0]\n",
    "rms(np.matmul(X,theta)-price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x136585400>"
      ]
     },
     "execution_count": 1115,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13638b048>]"
      ]
     },
     "execution_count": 1115,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ujBh6QWhFfMXi22yi8qmn4LHHwGpt2eMKHQ4x9ILQSvgrGho9amTbTFSuWAG7dkFUVMseV+hwiKEXhFbCn5jZ1g+28+yShUTseYXDT1xNxJ5XeLalJio/+gguv9zw4sPCoEePZh9SpAw6PpJ1IwitRPbB/aSN8xGLf30/48ff2DoZKHl58NNPhqFvAU9+6rTpPL9qHYlXzGqbDCGhVRCPXhBaiTYtGjp+3Hi97jpjEjYlpdmHzMxcy4oXXybxilnBLbEsNEhAhl4p9aNS6r9KqX8rpfY41yUopbYppfY7X+Od65VS6kml1AGl1F6l1DmteQKCEKw0pmioWeGRrVvhpJPgiy+MZUvLPKjPnfcg9qry4JVYFgKmMX8RF2mt8z2W/wh8qLV+TCn1R+fy/cBoIN35cz7wrPNVELoUgRYNNbuAyqVdM2BAi44/++B+QhLSqMrJ8sr5FymDjkdABVNKqR+BwZ6GXin1HfBbrfXPSqkewCda61OVUs8536+rvZ2/40vBlNCVaXIB1eefG1IGrVTpelL6aRQmn0151ickjr6bsN4DqcrJomDzIl5e/pTE6IOAli6Y0sAHSqkvlFKTnetSXcbb+eoKCvYCDnvsm+NcJwiCD5pUQPWPf8D558PKla02rvnzHkAf+JTIgb+lcNtyDi3OIP/th7n95hvEyHcwAjX0F2qtz8EIy0xTSg2rZ1tf7kWdxwal1GSl1B6l1J68vLwAhyEInY8mTdqefz488wxMmNBq4xo//kaeXbKQhLx/YyvKod/Jp/DKyhUse+bpOttKCmZwE5Ch11ofcb7mAhuA84BjzpANztdc5+Y5QJrH7r2BIz6OuUJrPVhrPTg5ObnpZyAIHZxGKT2+8orROEQpuPNOiIho1bGNH38jP+z/Fofdzg/7v/XpyUs3qeCnQUOvlIpSSsW43gOjgP8BG4GJzs0mAu84328EbnZm3/waKKkvPi8IXR2X59xgAdWRIzBtGixa1D4D9YO/wjBJwQweAvHoU4G/K6X+A/wLeFdr/R7wGHCJUmo/cIlzGWALcBA4ADwPTG3xUQtCJyMQz5mePeGzz+DRR9t+gPXQZiJtjUBCSd40mF6ptT4InOVjfQEwwsd6DUxrkdEJQldHa/jrX+GMM+B3vzNUKIOMvv3TqQiiFMw21/vvAEhlrCDUIhBvsM08xupq2L7d+AlSgq2blISS6iKGXhA8CGRisU0mH7UGm80QJnv//VZt5B0o/m5uAc8xtBHBGEpqb6TDlCB4EEjxUqt3iNLaaOB99Ci8+iqYzc0/ZjPxDIe4CqfKP3y6XQ26P9qlg1c7IR2mBKEJBOINtrrHqBT072/o15iC41+0I4VDgi2UFAwEx1+RIAQJgRQv+dvGEh7VvJi93Q6HDhnvZ8yABQvapJF3IHSkcEiwhZKCATH0Qpemdtw5kO5PvjzG/E0LiThrTPNi9vfeC+edBwUFLXyWzadNJZdbgIDSVbsQEqMXuiz+4s4Trs1g6wfbyT5oKE7On/eAT8XJufMeJPvgfizhUUScNYb4YTe5P29STPibb2DbNiM+H2R0pBh9VyLQGL0YeqHL0lKTdiazmbR716PMJ8pStN3G4SeuxmG3179zVRVs2QIZGY0ef1vjeXPzdwMU2haZjBWEBmipuHNTwxqZmWt5pFcaXH01o/v0C/rqTQmHdFzE0AtBTWsWJvkz0InJ3Rv1nU3J8nCFQpaN+AM3XfP/+OrCO/zG9aWcX2g2Wut2/zn33HO1INRmzZpMHZPcU6de/4juM+ttnXr9Izomuadesyaz1Y4fHhOvI+JTG/2da9Zk6n4DTtXKZNL9Bpxa//alpfqF2Hjd/5r/p/vev9n9k3r9I7rfgFMbHGNLXoOOSKOudScH2KMDsLESoxeClrYofKkdd7ZarZiGT23dYpuPPqJixAjuuOYBdg44z73aV1y/KxX/BELtSeHiXeuwfrUZR1UFfU/uevMGEqMXOjxtkbtdO+6cf+xI632ny6m6+GKG9zuZD0LCvT72FdcP5Br4Cu101nCPZ+FW+Xe7KM/6hKRxc0ibKTr49SGGXgha2iN3u9W+s6AAhg+HHTsAuHv+gwHF9Rsajy/dndvunM7td93bKRuBeN74Sna/RuLouztEtW57I4ZeCFrmz3uAkncX8tNzt5O94Ep+eu52St5d2Kql7K1WPm+3g9UK5eVA4NWbDY3HlzSBzRxOt0s7pwH0vPHVFOR0mGrd9qZBPXpBaE+UJZTES+9yF+kcf39pq36fy9DOnfcg2a8bcfvFzSkKKiqCuDhISYHPP/fSrhk//sYGj9vQeLIP7idtnLexs5Uc820AX+/4BnD+vAcMbfkR0wlJ6E1VEOngBzPi0QtBy9x5D9bxTLtdenere6aNyRf3FwvPzFzLoP7pfJeQwHMJicb6JgqU1TceX6EdS2xqh5IraMx8gueTUE3hYQo2LxLxsgAQQy8ELcEupOVPl37qtOncOWM2uef9H+//+lo2n/v7VouR+wrtWOyVHH9/aYcwgE3R9nfd+LTDwcvLnxLxsgCQ9EohaGnp1MKWLuE/Kf00CpPPpmL/bmoKcghJ7E1E+hC6f7WZyFHTKTp9aIuMuyF8nRfQIeQKJH20eYjWjdDhaUkhraYcq6EbgzKZMHdLIWn03e5jFm75G18ez6W6x6lcfdMit8xwwNo3XYxm6QQJkkcvdHxaUlf8npmzqajRHHttLj+//Afs1iK/mSiZmWtJ6ZnGhAkTyMk/TsLoe3yGFEIiokmqld6XMOYe7ggJY+ZZo7y05FtEr74T0tHkjzsqYuiFoKYlhLQyM9dSWFpO4mV30WfmehJGTqF45ypspfl14v0uz980fCp9Zm0g8bK7KPl7ps8bg63C6p5DODXvR674ZidhvQfyWU01X3zxVr169bffdS/J3Xt1ecMv3aDaBjH0Qqdn7rwHSb7yPi/PO3H03ZTsWlfHc/SVl544+m5Kdr9WZyK478knvNE/7FrHHz95CfXjf+g34BSvJ5HCjY8SNWgU8cNu8soeKq7Sna6gqbG0RTeozlol3BjE0AudCl//1P6yd2zFR+t4jv62rSnIqRNS8PRGZ156FxnDJlG44zl3LN/1JGKrtBJ34Q11v7/kWKcraGoKrSl/3JSsns6IGHqh0zB12nQmTbmrzj91UmpPn3Hg5B69GD/+Rq+bgyU8ync/2NjUOiGF8Sf14z/p/ej2+cvse/pG8r/d6NMb9ReHDkns7V4OprTRzkRHamremoihFzoFU6dNZ/nKl0i8Yladf2rtcPiMAy9Z+Hgdjy/irDHkb1rotW3exgXEham6RvzrrzkpP599f99Rrzfqs8fsliXEDrnOvU1TdPCFhgn2Woy2QiQQhA5PZuZanl+1Dl1T4fOf+nDeUVavWu1TRuCk9NPcHh/g7vtauPFRbJVW+vZPZ9WKZ7wNeGUlhIfD7bfDhAkQEVHv+GrLGCSl9iRE2zBHxaPtNqpysih5dyHKEop58ETSxg2kIifLKPX32L8p16Wj5te3FH37p1MhMgmSRy90fFxFN4Xbl5Mwckqjim8ance9bRvccgu8/z4MHFj38wBpig5+Ywq+fNUNHH9/KdpWTezls7tMg+/O3tRc8uiFDk1jMiVcj+exQ66jYKt36X/B5kX1puo1Oo+7f384+2xITW3SebnwnICcP+8B8n7+qd4QQ2MnFX3Fprtdejc2c3iXile3RVZPRyBgQ6+UMiulvlJKbXYun6SU+qdSar9S6jWlVKhzfZhz+YDz836tM3Shs1LbqBUmn83E2yZjMvk2+i5jHTVwOHHDbqZw+3IOLc4gd/18br/5hjr/1J43kbLS0sB0Yb51PhGcfDJs2gSJiS16rpa47vXecBo7qeg306jkWJ11nT1eLU3NG+fR3w1847H8OLBEa50OFAG3OtffChRprQcAS5zbCR2c5uQiN3bfxnYR8pzsjDz1QhJGTsESFc+U2/6PZc88XWcsnjcR80XT0bZqHDuW+ff4du+GM86A1asDPudAr8U9M42wQtzQCXWeRjxvOI2dVPT3pGKJTa2zrqvFq7siARl6pVRv4HJgpXNZARcDbzo3eQUY53x/lXMZ5+cjnNsLHZTm5CI3Zd/GdhHy9Xj+8vKn6hh58O0Zx14+m6ioKP8e33nnwUMPQUZGgFcs8GtRWFqOrTS/1tPI1eS+9ZDXDaexISZfmT7H31+KxV7ZalWoUpgUvAQ0GauUehN4FIgBZgGTgH84vXaUUmnAVq31GUqp/wGXaa1znJ99D5yvtc73d3yZjA1umqMw2JR9PffJXnAlfWa2nOhVoyZf33oLLr4Y4uMb/T2+8HctCt57il53PO+1rvb1aSlRNmidrJvOPukZrLTYZKxS6gogV2v9hedqH5vqAD7zPO5kpdQepdSevLy8hoYhtCPNyUVuyr6jR410N5RwdRHypLYn6+lJJnfvRUrPNL9eZcCecU4OjB8PjzzS4DkGSn0Vug152U2ZVPQVm26teLUUJgU3gYRuLgSuVEr9CLyKEbL5GxCnlHK5Rb2BI873OUAagPPzWKCw9kG11iu01oO11oOTk5ObdRJC69IchcHG7puZuZY1b2wg8sxLKNy2nJqCw+RtWuDXEHqGQxJG30NRRQ2m4VP9TuIGLKLVuzd89BHMn9+IK9W0a5Hco1dABjyYJxWlMCm4adDQa63/pLXurbXuB1wPfKS1Hg98DPzOudlE4B3n+43OZZyff6SDIVlfaDLNURhs7L4uzzB+2E30vG0Zfe/fRPSgSync+KhPQ+jpSR7/55skjZlR7yQuUL9n/MQT8MEHxvsLLoCwMJ/jbEo82t+1WLLw8aA14IEicsNBjtY64B/gt8Bm5/v+wL+AA8AbQJhzfbhz+YDz8/4NHffcc8/VQnCzZk2m7jfgVK1MJt1vwKl6zZrMVtlXmUy6z6y3dd/7N7t/+sx6WyuTqcHtUSfehyT10anXP+J1nNTrH9H9Bpzqf6AVFVoPGqT1pEkNnk9Mck+dev0jus+st3Xq9Y/omOSeAV2T5lzHYKY510RoOsAeHYDtlspYoc0IpLIz0Mlb97GyD5FyzV8I7zuIIy9MdVfGNmoSV2vjx2SCoiKIiQGLf3UQf2PMfesh+vbt0+llBfzR0q0ahYaRVoJCUOErK6Pk3YXEREeRf+yIV1bInTNmowYMpWLfbmoKD2MOi2TyLZPc6ZKex7KV5lP86WqSxszwel+4bTkJlwQgh6A1/OlPUFAAzz1nGPsG8Je5c2jx1aReN1+yTYQ2QyQQhKCidlaG3VpEjbK4J049Y+gTrs2g/L/bSLhkCn1mbiBp3BzWvLHBHQf3PFb0GRcTP3wSBe89RcG7S4iPCMGxYxk1hYfdmTv1zg0oBSEhxo8TV/xdmUyERnWrU5Fbn+ywZJsIwYh49EKbUNsL9gyzuHB53EC94ZtAc+HrDSU4HJCfDykphlcPoJT7aUENGIo16xOvxt8uTx2o83RSsHUpccNuJmrgcGluLbQZ4tELQUVtL7imIMdvOl5DqXr1ZXh4ZsPMnfcg8+c94M5mAdyfrUxMouyMM4yYvFLuRt6up4WK/bvrNP52eeqeOe2HFmVQ8N5TbiPvORZBCBbE0HdxWrps3d/xaqcWWmJT/RrrhlL1/KUpjh410q/cQm35gdfPu5EnrJVkvrvF63tcN5n6bkRwIqd9zZo1RIQot7a8NLdue0R6oWGk8UgXxnNSsyWaXQRyPFfzjcTk7hx/fylc6h0aWewRGqFWOb3rs9rHcjUSuWfmbCpqNKWvzSUksTexQ67zipd3u+hOhmkHn5kt7PvlaPYm9CLirw8xfsJ49zm4GlWYuyVTFUDDCn9jkYnYtqGl/4Y7LYHkYLb2j+TRtw/9Bpza+FzzRhwvaexsbYnroUH5zBn3zClP7tFbJ6X2dOeX3zl1WqPyzdesydSmyDjdbch1OiSxj0YprcKidPTZY7QymbQymfSjQ2/SdpQeecszfvPz16zJ1Co0SquIbtrcLdkrL9wUGaeTUlsmN7yz5tO3NS39N9zRIMA8egnddGEaU7YeyOOx5/GsWTso3rmKxMvuos+sDT5VK13hj9WrVlNpc2C+aLo75LLmjQ1e8XWXd+ZvHHPnPUiH9nVtAAAgAElEQVT0WZdSnvWJO1snJWMO5ft3k5jcnb7901meOoCp4/7I/uS+gH8P3WSClKv+SPzwSW41yYL3nkKZLJgvmh6wcqc/mqMGKngj0guBIYa+CxNo2XqghsnzeIHIC7sIVBCrvnFkH9xPxb7ddb4zbfQ93G8t5ZE//5HCHc/xdnhMg7F0R5XRezZq4HB63rqMvvdtpOdtz2K3FjY6fdLXjUkEwFoOkV4IDDH0XZhAdWjqM0yZmWtJ6ZmGUiays7PJ2/AIldl7G5zM9CRQr6y+cfTtn05N4eE6xxnusHFPWSk39OgesPpj35P958nXdx618Xdj+vH7fc3yQmXy8QTN0WHqSoih78IEKn3rzxD/+P0+br/rXkzDp9Jn1gZSrnkAFRpG7lt/RVnCAva0AvXK6rshzJ/3AOawyDrHeT80gguTu3PSXfdw0803AbB61ep6xcN8GY+8TQsJ7zOo3vOojb8bU0hEdMBPUrUNuoR9vJGesIEhBVNCg/jTdinc+CgJV/7JZyONuDBFlYOAGlEE2rSiIR2cqdOm8/yqdfQbNZ3nvnqXR9N/za7P30Tbqom9fHajGmJMnTadFS++jL2qnJCENCJOGYI16xOiBv4WfeDTgIyJ38KuxVcTndS93vP1d03CLSZMw6c2qQmM0PmQgimhxfD3eGyrsPptQF2Qd5RnlyzE/vHTHF56A8denUO4xfefW6BeWUOP6cueeZqXlz9F8hdr6P3DF8R+8gIVx4uIvXx2QPF/T+/5zQ3vkDRuDn3v20TP25YRP+wmkkbfTcV/tgTsMfp9Ujk5vcHz9fc0kPfzTzL5KDQaMfRdhObEdf0ZYn+xbEtsqjsMUeWAlGv+Qp9ZGzANn+o3zBBIU43x429kwrUZFG58lEOLjNcJ12ac2NZqZfyNNzDt4YcYktSDv1/9ADhsDRpGX+EQfwbVVmkNOCxQ342pofP1F6ZSIeEy+Sg0GjH0XYCWiOt6pkIC3HTzTZSVllK89QkvQ5a/ZQkWeyXz5z3Q4tklru5TCVf+iT6zjFe32FlxMfz61/Dww8yd9yAhI+8ivO8gQhIbbkXoa5yWuO6NamHo6+bZnPixv6eBxIR4mXwUGo3E6DsZvoS85s57sMnNvWsf25fUcGiIheOF+aiQcBIT4vnbYsOYNaoRdwCclH4ahclnU7F/NzUFOYQk9iYifQgJef/mh++y4A9/gIwMTKNGub+3cNtyrN/tInms/xi9r3GW/e8jij5+keQr7/O5X2s3w67v+NA6Db6Fjofo0XdB/BmH0vyf6TNzg1+DG2jDiECbgjR1+4bObcLE/8MUFullfMPefQJraT75Hn/Hru+1W4so3rmKyIG/9attX9848zc/gaPKCvYqL738ufMe5McD+7DEdSdu6AS3mFlLT4pKI48TyLXwjUzGdkGaks7XmLBOY6sQfcWoCzYvYvSokY06L9cYLTGJJF95n/v8ItN+wQfKxFsm8wmpYY/vLf50DYmj73b3n026YhYqvBvPLltWR3CttnZ9wdalRJ05gr59+3ipX7quVZ9ZG0i87C6Kd67CmrWjwWvRFIK5GXhbIimlzUc8+k5EU9L5GhPWSemZ5jO1z7FjGblHDvsck680xUDTE124PO5jr82t0x7wN99/zr43H+Rf2uG1T2bmWiZMmECfWcaTjFuSwYe+/PjxNwY0Tr9pptuX0/PWZZLm2Eq05JNhZ0M8+i5IU9L5GuOlV1aUk79lSZ3J18qKcr9j2vrB9jppioGkN3p6a64xuiZW+xfk8NvvDcdguyWMvAGn1Pne8eNvpN+AUwKWZFj2zNO8snIF/U4+BVtRDgl5/65zM/J3rWoKcijauZr8tx8m+/v9Xb5ataURPZvmI4a+E9GUdL7GaIWUFhcRN/Qmt9BX4fblxA29idLiIr+GOpB/Us9H84TR95CTf5wJEyaQ0jONzMy17jHGDrmOgq1LuX/L33j4/afRB7+g5N2FWK1WnzcIz+sRiCRDQ6ESX9eqeNc6VEgYx3e/jgrvRsKYeyS00MKInk3zkdBNJ6Oxk1aNyR4xhUaScs1f6jxCH3tjHjEJSXWOMeHaDFasfBGH1uiaKsyxKcQPuxlzVLzXY3ftydPa4ZUJ12aw5o0N7mbg6tNMEo4f4+e4BGwqhG6X+g7HeF2P7EM+x96Yx//a16p41zqsez8gySOjx9VSsPY5Ck2ntTOcOjKSdSMETKA3h+TuvSiqqCFpzAz3P1z+liVQXU7SuDleRrRo52rKvnwXFRbhvf27iwnBwcpnn66T3vjzy3/w20f2mYk3kb9oEbccLyHt5FMYPWokK19e5VOCwZeBbSlj4XmtLOFRPr+/cPtyekx6UvrGtiCSdeMbMfRCi+D5D5aY3J3i46UQFo2t5BiW2FRUTTk11uOEJKZRU5jj7uxU8tlraHsNiZfd1eDkbX2Tre400IUL4cknYfduMj/6mDtnzG4wbbS+c2kJY+Fv8vvQ4qtJvW6+ePRCqyOTsUKzqR07L67S2CrKsFccP5HOaLdhjopzNvtYT8LIKRTvXEVN4WFsJcd8xsXzjx1xH/+k9NP48ft9FGxe5LOPrO3Qf41Y7L33wn/+Az16uNNIQxLTGhW7bWy6YkOVr/5ix5bYVKlWFYIKMfRCvV2bIkdMx24touTvme5uUSkZc7DEphA3dAI6vBtJY71FwxJH340Kiai3AbjnTSRxzAwcDge20nzyNi5wTyaf/fk7fPzWX/nbnXcYO8fGkpm5lh8PGHrursnZ1pAD8Je7PXXadPe1Kist5fj73t+ft3EBcWFK4sdCUCHNwbs4tfPHC5PPdjdXzj64n7RxA/n55T+4UxMBtzEv3L7cr9euqyuwm0PI37LEK0aft3EBq1Y8U+cm4qp2Ld61jvy3H8ZRVcHpvfsQmz6Aq268AThhfM3RCVTlZLkrUgu3L6em4DCm0AhWvfB8ixhYz+Iz1zlXDBjK86vWkXjFLNLGGeej312IY8cyDh87Qt/+6axa8YwYeCHoEI++A9MURUrPfZK792LFK2tJGjeHPjM3kHDJFMqzPkENGOru2lSVk+U3NbGmIAdzVLzvbkyR0cScfRloTe5bD3FoUQb5mxeTEBPplb9fO789fthNDLpkGqawCD44eozu335Lyjm/csfX1YChaLvNnc8feeqFJIycgjk6CUd1RYsZWV9poRX7dpN4xSyvp5fYy2cTFRXV5atXheCmQUOvlApXSv1LKfUfpdTXSqm/OtefpJT6p1Jqv1LqNaVUqHN9mHP5gPPzfq17Cl2TppSF196nuEr7DLtU7NtN9sH9jB41kvy3HwatObLyTnepPxjGHHMI9soyr3BLZfZejr+/lNsm3Yw+8ClJl99L2t3rSL3+YUKUA2UyYTKbsYRHUbxrHTUF3u3/zvnpGz7bsoSMSivaVok5OonC0gomTJhA9qFDlO55h+Sr7q/TuFvba+h3ct3CqabiK/7uq1VhVyvckTaGHZNAPPoq4GKt9VnA2cBlSqlfA48DS7TW6UARcKtz+1uBIq31AGCJczuhhWmKBHDtffyFXWoKD5OY3J01b2wwvH2nrkvRjpcp+99HVGbvJfftxzCFRpD6u/9H/EW3UPDeU26vPSrUzLJnnvaqxrV//DTKEopp+FTS7l1PwpV/wrr3A1RIhJdB/V/qAFamD+HjqHgSx8wAkyLqzJGYY1NIufovaFu1z8bdjvKSFp389FV85qtVYUOFO/4MY0cymO6xmsxMvG0yhclni+ZMB6NBQ68NypyLIc4fDVwMvOlc/wowzvn+Kucyzs9HKKVUi41YAJpWFl57H39a7eawSJTJVOdGkjRmBoUfLCN/61Jw2NwCY9FnXEyvO54n9fqHcVSVU1BoVMp6ZrlEx8TQ7VJvCYKksbPdYZjz//EW4RVlHP/pG+458g3FJjPH//kmSWNmULF/N0nO8I6/MavQCHZ99lmD1y1QA+tLS37yLZMapQVf34RuRxHp8jqHmetJGjeH8qxPKP9uV7P7CwhtR0AxeqWUWSn1byAX2AZ8DxRrrW3OTXKAXs73vYDDAM7PS4DElhy00LSy8Nr7xA65ro52TcHmRUy+ZRL5R4/4nmS1VWMKCUPXVPj5vIqUa/7iNlzuFMoD+wxt+KwdWLN2cOSFqRx7bS7Ya/jF4KtYveMlJj15vVtWwV5W6J4b8Jwj8JVpk7dpIbq6guUvvMTUadOBlmmsXTsds/ZTSkONRPw9da18eVWLNmRpTXydQ+LouynZ/RrQ9UJXHZWAsm601nbgbKVUHLABON3XZs5XX957naospdRkYDJAnz59AhqscIL58x4wsmNqVXoudjamCGQfc1Q8IdrmlTXy8vKnAFjx4stU5WR5FTu5csRrCnIISUjz+XlIYm9j3Yjp3DNzNlUOUAOGElJUQU3hYfK3Pok5PJqkK2YS1nsgPy2/lWMp/bn92r/yz7Rf0DMk3AiTdEvGFBLmPqbru1yZNgXvPYWt+CgqLJKYc64g7sIbqMrJ4vlViwDckglp4wZSkZPFnTNmE2aiTiYNTgMb6CTq+PE3BrytK2vJk7DeA6kpL/P9NPZ68BlMv+dQkAOI5kxHoVFZN1rrYuAT4NdAnFLKdaPoDRxxvs8B0gCcn8cChT6OtUJrPVhrPTg5Oblpo+/CNKVNna99Vj77NLlHDntljcyd9yBRv7yijreft3EBtrJCLLGpRJwypI5nXbB1KbFDrgMMY1BQWIQaMJTyrE+cBVUbsEQnkHTFTML7DmL8f7dxvsMI3bxvDqHCZDHi/+88hqOylJqCw+RueBhLfE/ynd9V9r+PKP50jZeRjx920wlv84pZfj3mgsKiZk+mNia27u+pKyTSf3+AYMPvOST0ljaGHYgGPXqlVDJQo7UuVkpFACMxJlg/Bn4HvApMBN5x7rLRubzb+flHOhh0FjohjfEuG7NP9sH9JJx6Obqm2vCcnXIH2lZjTOKW5lP2n/eJPutSCrcZOeyWuO7EDbvZ7XFX5WShayqNlESPHHzXBHB4TSW3/2s9p5WX8N3l9zpz4XMwRydgsoSRdPkfT+Teb1qIw1pM7lsPokLCvTpM5W9dSmhSH/f31ucx65pKn08hgRpYT70czycF13Wtjb+nrtsm3cyaN55u1NNYe+HrHAo2L8JmLSJizysslsKwDkEgoZsewCtKKTPGE8DrWuvNSqks4FWl1HzgK+AF5/YvAKuVUgcwPPnrW2HcQivSt386ObvWkXzV/XV0agree4r4CDNLFj5u6MYU5ZCU2gNrtR1zVDzabnMbruQevcg7erjuBPDhr1H9zuL3Ny4g69U/ExOTRM9blwFw5IWpXsJm4X0HkTx2NoXblwPU+SzJWbjleYNRzuyY2gY9uUcvyj9smoHNzFzL/02eQk1FGZXblxM75DrjO+sJ/bjWzZ33INmvG/o6LsN44QUX+FwfbPg6h5eXPxWUYxX8I6JmghtXUdKPB/YBkHj5DI7/8013I+5u5/+Ogi1/QynqiIb5EgwDmHjbZC9lyylvP4rlhy9ZlDGXsLRfkPfOY1Qd+ZbksYaXfmhxhk+hskOLrwbwKXrm2sclExxx8q8oP/BPr4rc5jTW9qV86ZIjjjz1woBUKkV9UWgNRL1SqJfahmf0qJGseWMDasBQrFmf4KgsxxQW7jaWxbvWUfrlZnRVOSGR0by0YrlfQ+V57OjoWMrtGJrtvU5n7prZhOQe5FZzCA5bNaaoOKIHjXI371YhEaRcPbeu9O+25X7VMHPXP4SuqXIrZ0YNHE7Z/z6i8INnvRp7N9Ww1tdCMGHklAZVKkVPXWgtxNALfvFleHI3PIwpJBx7WSGWuO7YrCVYomLdk566qhxLXHdiL7wBS0ySX0Pl69glmxfQMyqSg7k/ExIZR+IVMwlNO4MjK++sY7iLdq6mbO8HJHs283DGhJNSjBBR7UYj1FQSedmsRvWybQz+5YgziEnq0aDBlp6nQmshMsWCT1yxZs+sFLu1CFNYJElXzKTPrA1Enj4MU2gYkacPMypSM05Ux5b8PRO7tchv3rdn3nX5d7so3L6c/1dWzKbco/SKSyBh7GzC+p3ttzI37sIbcFiLKX9vEYeX3sCxV+cQHxPJmtVryDv6E88/9USdTKOwsHCfvWy1w1FnfL6uR0NZNH4zTyKiA/LKpeep0N6Ioa+HjlSmHgiZmWu5/a57qanwzkop2f0aSWNmuA1/xf7dJI+d7VWRWrtYxp+hchk1a9YOineuImHkFL76/UNsP20oPxUVNFiZW7xrHebQcKzVDlKu+Qt9Zm3ANHyqu7DJl6Z8Qd5Rn71sC/KONng9Aimg8teLt77wlSet1fO0s/19Cq2HGHo/NEU0rLnf19r/tDNm30+3S++u07Cjtjqlr4pUF671xbvWYQqNRCkTptBIkrv3Yuq06VjCozi0OIPiD5bxm7QzCe87iH+e9EueuHI2lrge9VbmFu1cbejfRMa55RX8VY56Xi9LeBQWZ+ZO3/s20vPWZVhikho0pIHqBTWlZsGT+pq2N5W2/vsUOjYSo/dDW8ZV22qyTikTfWZtoPy7XV5NuGvHyl0pjq7JxtrXIH/zYtAOr6bYue88hslkdq+74/1lzP7vBwy96FaOnpcBQMH7yyjf95lXHnzuhofBYTeah4dHkjRuTv0tBe32gJp0B5Jl4y/23pK9Xt2ZTN/vIyQiGluFlb4nNz/rRuL+AkiMvtm0ZVy1KUqU0PinABUS7m7YETfsZmeoIwNbaYGX1HBE+hDyNi0kIn2IuyLVszrWUVlWR97YHBbltW7tiNuYfd41fPnfbQBYs3ZQcfBzd5HVocUZ5G6Yj64qB6fmnb2ynLDeA/0Kl7k89NrXK37YTUQNGkXhxke9PG6gXq+3tUIqLjy97j4zN5Bw5Z+ITureIqmVEvcXGoMYej+0thHwxDOufeSFqWQvuJLCbcv58ft9fveZOm06k6bcVe+j+9Rp0wmN6oZSJkKjuhEeGlK3YUdMEspsQdtryN+8mEOLMij/ZieR6UMo/2Yn9pJcctfP59CiDKNY6qJb0PbqOkbGVnKM6B7p3PqvDZgddsrCItkw7CZqCg6j7TaKP11D0pgZxA+7iZ63LaPvfZuIOWcspqhYYs69kpDENJRT26a+FoGZmWvJzj7EsdfmcuSFqW6N/JCEXthqbF5jaugG2hohlcZ8f3Noy79PoeMjht4PrW0EPOnbP53iXevck5d9Zq4n4ZIpWKLifXrpmZlrWfHiy3W6HXkakanTprPilbUkXPkn+swyvMlKmx1HZbmhHe9s2OGoqQLtICVjDr2nvULS2FkoSwhl/9mKvbzE/Z2p1z9MRP9zKfpwBcoSVsfIWGJTGfr52/zl4xf4zY//Bk5kphxanIGt+KjPjk3Rgy51a+EkjJpK/pYlmKPiif3NeLfGvWPHMi8PPeWav9Bn5noi0odQ8MEysh8fS9EnL5FyzV9IGH0POfnHjUYl2YewleZ7faen19vc2HtDNNfrru+JrS3/PoWOj8To66G1qxndx/9+P4SEE3PuWOKH3eT+3FfM1V2KX15GSGIasRdc5y7/94wvh0Z1I+HKP9WJ4R5786+GB19djrKEkzDqTgreXUKfWT6qURdlYI5NwX48l+izRlPuzMaxleZT/Olqr8rT3HcewxQSxvAh13HgzJFOjZoFXHTBr/jXv7+moka75wGsWTso2f0aNfmHCUlMI+GSE/MA1qwdbtGyfgNO8brmKT3TMA2f6j6Ga56hcNtyEi6Zgt1a5DX3UJWTRf6WJcQPn+S+Ri2ZX98QzYmjBzJvI9W2gsToWwBfqXwtRe2GDilXz8Wa9YlXu77a3p9rH7eXfskUineucu/jenTPzFzrV9gLWzWm0Agssd0BjSUmCVN4lN9mHkmjjSwd6zc7SHbF4E1mZy/YB8lfNI4lr83lvPOuJnLA+Xz8yUscWpxB4bblRA+6lE8+/YzIEdOJGzqBgq1LKdq5mqKdq4hIH4IKi6zTni9q4HB63vYsgJfhysxcS97PP7m39ew1W1OY47P/rKtZSvGnaxrMr2+NrKfmeN2BhH1a8+9T6FyIoW8nfP0jJ3k0dADvmKvLky/N/5nC7csp/24XdmsRKBP5mxbx03O3k7v+YbJ/+IFbp93tFvbyxCX4ZS8rpOdtz2IKjyZ/yxLC0s4gb9NCn808wnoPJLzPIHSVMVFauG05hR+tdPaCfZUzL5/JMDSnHfmOykN7ScmYQ9/7NtHztmXED7sJu3M/1wRw6ZebSRp9NxX7dxNzzhWoUN/jtMR19zJqc+c9iCWuu3tbz9RP1+Stv3RQW/FR7/z6XO/8+tZKVWxOaEgmW4WWJKDGI0LL47+hw2EvBcjFSxZ6efKeIQldU03yVfefWLd5MfZKG3Gj76V832fkbVroJSWQv2khJjQqNpWqnCzsZQUkjjGEyxzWYnLXz0dXV6BCwwnvexa2oiMU71pHxfefo8IiKd61jrKvPyYlYw4xvU+nxmzh6BkXMTQihh83LURXl9cxTrUblLhuGDUFOfSYdAO6ylpnnAVblxL7m/Fkb/2b1/VKGH0PBVuXkjj6bkISTjQjcU3eWpznVacZSlKaWx2zMnsvlogowFvETYVFUvraHCMcNuQ6t/fcXC+5KVLSYMzbVDRDUlkQPBGPvoUJNARQX1l9be/Pp/c/ZgamsEivdVFnjkSZTBx7bS6Vh/YSmtyPvLcf4dCiDHLXP8RvLxhMSGgY9vLj5G1cgAqNPFFodP8m+sx4ndTrH0bb7VTn/kBE+hBKv9xM4ui7if7FRZR+uQldXU5Scl/eXHMf/7fHaEFg73c2urocU1jdEFDEKUMo2LyIyuy9lHz2mtsrd3nhCZdMIeHi29ypnnlvP0LcsJvrFDz17Z+OJSbJnRZaU3DY/RQSeeqFRA78LbayQq80UdeTSUT6kBOhm61Lqakoc988C5PPPiHzMHMDCSONcJitNL9dvWeZbBVaEjH0LUhjQgD1ldW7Yq6Au9+qz5BEyTH3stGL9RNSrjYyUhJGTqE670ccNdXOLRQfbttOjTahzBaiz7oUXVVeJ08+f+tSsNcQNfC3VOzf7fbAEy6Zgq6qICQhjeJjB/khoSfZcT0AV0PxKByV1johoJpvP+H2m28gYs8r1BQcJvbCGwwpYY8cfc9Uz/gRkzFHxZO3cYGXUXNdL3NUPD0mPUm3Ib8HWxXHXp3D4aU3EHrwU+6cfBuhZuXOKsrd8DBhPU+lYv9ud+gmauBv6XfyKe6bp1+Zh13r2tV7bu2MIKFrIVk3ARBodkNjsiwyM9dyz8zZFBQWoWsqSe7RiyULH/eafHRlXbiySnw1AYkbOoGS3a9hK8kj5Zq/1Nkmb+MClDmEpMtneIR4FoEyYS8twBydAEphLyskJLE3EelDsP53O5gtRlMPj++2PX8HnHw+x/bt8spsKdi8iLiocMwXTcduLTIyagpysMSmEhemyDv6k9f1cW+Tf9itjGmOTQGH3VDPrLVf7d/Dj9/vwxIVT+IVs9xjOP7+UqJCzeTn/uyuQE1M6e5T7fLZJQu56eabSLt3PYcWX+1b435RBmvWrBHDKgQ1IlPcQjRGniDQkvpAjul50/BMJTyhDb8JXVUB5lCUSRkSAt2SiR8+kaiBw7Fm7aDo45dwVFtJubruDaDgvafoeduz7nh/RP9fUfnjV9iKj2KOTSHy5F9ReWgvNfmHMUXF0v3ymXywdSk55SX8/lcZWP/3EY6qMnRNFSokDF1T5TNF0/PcfZ13/ruL0Tab11xDweZF9XYx8ndD9TynhiQQXMfwJ/PQVimYgtAcxNC3EI3x0gPdNpDtTCYzaR6epjVrByWfvUZNwWF3s47Sr7ZiCg3zymfP37KEyAHnY/3mU1RIKPbSfL8dm/retxFwasD/530vDRpXByXXd6qwSK6uspIfEctOhwNlNnttn7dpAdGDLg2oDsBleJNSe1JaZiX0jBONR8xhkUy+ZRLLnnna7+/Evz78iXNqKF/dddNxNVpJGl3X6xdvXgh2JI++hWhMmlt9E2iek7QNVWwCWCK8JzajBg4n4ZIpqNAIksfOxpr1CebwKC95Ydckbdn/PkSZLSSNmVFHqRJwT4a6JBdK92ysoxbpkiPuWXCI4d2SiTnnCjYm9WFHZSlK6TrbJ4+9j9I97/DTc7dT8P4yfnrudo69Oger1eo1R+HK/Z4y5U6KS0qoLC2m7MtN1BQcpt/Jp/DKyhX1GnmoZyI7sXeDvyPPcTy7ZCEJef/GfjzX0MlZLLFwoXMi6ZUN0Jg0N3/NoAF3yCJt3AnPW5nMXk2tPY9ZU1FG/talXp5m3qaF6Bojt91ekgtK+bwJ6epK7NWVhPUe6E49rF0tGjngfAq3r8AUFomuqayrXVOaj60kl2eBX5Tmc8rnG9HRcQA4Kq1ubR5XPD4koTe6porEy+4ib9NCogeNIu7CG6jKyeLOGbO9ro9LniHJM11000JGjxpZr4H1itEfXeQVo3dVwDb0O6r9+xKDLnQFxNA3wPx5DxiGqlY83WXAa+PLeJyUfpo7PRJwe94F7z1F5KkX+jxmv5NPoTD5bHcqoQqJIObcsVTs320UPoWEY46K85k3rkIjMEfGupUqgRPHCY0EwPrt31EhoSRedheF25YbefUek6SmqDhSrnmAWXk/Evav9VSVFmC2VZM45h5Kdq2jeNc6yrM+8bqB5G1aiN1aRPLY2RRuX078sJuMsdXKSV/58iqSPOQZwvsOImnsbFa+/CgXXnCBz5h6ZuZabrtzOjZzOKBwOBzkbZiPrq4kqXtPQrQNc1R8nRoEQRAkRh8QzdUU8RtTXpSBMimfx5w6bTorXnwZe1U5IQlp1BQc9tKSd9RUobUDU4h3jD5v00Ic1mISL59Byd8zvQ3xxgVoux203RAyu+YB92Rv4fYVqJBQksbMoPvWJ7m51+k82v9cij9d7Z1hs1AyxgYAACAASURBVHUpESf/yl04VUer/t0nMIVGUlNwGHNMIpjM2I/noSxhrH5pJePH3+jWxfd1PWKSe/icpL5n5myKKmrqzEfER4SQd/Qn0X0RuiQyGRtENFbcyld2iudkpzVrB/lblqLMIShLCLqmCl1TiQqNIPqMi6k8tJeEkVPqpDraSvMxhUeTPHY2x16d42Vsc5bf6s4nn/j4WKZGxTE4LJKaUdPqjNv1dFB7krfsfx9R9PGLJF95n5fwma00n5Jd67AVHyW5Ry8Ki4pIGlf3JpG3YT7JGXN9Xqfs7EM+00dz33oIR3V5y/yiBKGDIZOxQYS/SdrRo0b6rKL1VQmbPPY+jv/rbXKemUj+5sUoi2FgXUbe3C0ZZQ4h8pQL6Hb+79xyvz0mPUnqdfPRDhvmiFi3MJk5NsVrQtN+PI+wXqdjzdrB/LBIRlwyhZyin/22ErTEdq8zIVqya517kvb4P98kacwMQ1Hy09UkXnaXu/+rwwF5m7wrWPM3LcTh1Nap/X3ZB/f7nEcI6z0QXVPZYr8nQeisiKFvA3xVOU64NoM1b2zwWUXrK9PHVpqPKSyCpCtmkjjmHswRsYbsQEQMpshYksbcQ8LIyRRuX07Blr9htx53NwzJ3fAwkQPOx24txFaaT87yW7GX5HrJBVwYFc/65bcS/slLRJ9zBd9+/CLmqHjfgmOxqdgrjpP/7mIvY+2pOe8SGCvauapOZlDK1XNwVFaQu/4hDi3KoHDjo0yeeCP9Tj7FbzON5B69fH6W3KNXnesdqAyFNNcWugoyGdtG1J6k9TVBy4jpzJh9PxanbLBnmMLlLdutRXVj75sWkvv2o6SM+xM9Jj1piI/tfZ/ksd558SosiuKdr5B0+Ux34VXuhofRVeWkhUVhqi4n5YpZmAcOQ1dZKfv6Y/K3LPGeA9i4AEd1Bd1+NY7QpD7OMI4RGlKh4e5xu7Rs7CW5vuWS7dUQGoM53ISt0srWD7YzetRI1rzxtN+J79vvuhc8qlyPv7+U5596wuvYnmGvtHEDqfCR9dOY7QShMyAx+jai9mThj9/v813ItCiDiPTzqTrynZeioyum/vPLf/BZyZm7fj7aXoMyWQDtnmj12mbDw14TqNasHZh3rOLY8VxCEtOwFRwibdbblH+3i8Jtz5I87s914vwRVFFaXOSeGPZMr6wpOIy5W5I7Ll/86WocFaW+x/LWg5giYtw3keJd6yj7cjOOqnJCIn030Q5kwrUli9YEIdgJNEYvHn0b4Mt7VIfn+0yNtMR1x1Z0xGjsseFhdHU5IYlpmCJi6tVc1zUVmCJjSR57H8dem+t7m6oTMsLWrB2c+tFK3quyclfGn9kaFkXuhvnutElHlZErr8yWOh2sTGERftIrFxCS0Nv9lGCKjEVrXeepIH/LEgB3SMeatYPyrE9Izpjj5cnXNuSB5L37k3/Ofn1/k7YThM5AgzF6pVSaUupjpdQ3SqmvlVJ3O9cnKKW2KaX2O1/jneuVUupJpdQBpdRepdQ5rX0SwY6vydWYc8bWbfaxcQGxF95ATUEOjorjJIy8A0u3FCLSh+CoqSL3ncdQoRE+Y9WmsCiSx97nFTbxpHjXOndoBYwOTUdG3807Z1zMbmsx+e8+gbbVUPrlJkPv3U9FbVJqTxxVFZR+salON6fksfdRfXQ/KRlzQCl6T32ZpNF/QNdUe/Wp1TXV6Joqn92imttEO9Cm2dJcW+hKBDIZawNmaq1PB34NTFNKDQT+CHyotU4HPnQuA4wG0p0/k4FnW3zUrUhrTND5mlyNu/AGHNZipw67IaGrbTWU7FoHWqNCI9z662VfvWu0ALSEEXPOFXWkhQu2LnVXqwLualjXNkU7V1O29wPC+55F3qaFnLlnE+Qfxt7vbO5JO5P9n64BpUi99q/urlK1j+Fqw1dcVIQpKtZdoetJWO+B7nG4bjZRA4eTMHIyWjvAGSaMv/hWv92iXNhK88nOPoRSJkyhkSR37xXQ7yJQHXfRexe6FFrrRv0A7wCXAN8BPZzregDfOd8/B9zgsb17O38/5557rg4G1qzJ1DHJPXXq9Y/oPrPe1qnXP6JjknvqNWsyG9yv34BTtTKZdL8Bp9bZvt+AU3Xq9Y/ovvdvdv+kXv+IVmFR7u/qNuQ6bYqK97mMMmlTeLT7GEljZ2tzTJJWIeEalDZHJ2osYbrbkOt0SFIfjTJpc0ySNkXGalBahUbobkOu05bYVH3mLy/XVaAfMpl16vWP6JCkPtoS18N97JCkPl7fYxxPaVN4tE4aO9u9red2vs4paexsbYlN9bqWhERoFRppjMkSps3RCcaxEr2PlTR2tjZ3S/ba19wtWYfHxDf4uwjk99HY7TojXfncOxPAHh2A3W7UZKxSqh+wEzgDOKS1jvP4rEhrHa+U2gw8prX+u3P9h8D9Wmu/s63BMhnblAm62sVNxbvWYf1qM46qCvdk4q7PPjO0XTwmV/M2LkA77JjCIrGX5GIKjyJ53J+9vrto52rKvnoXbbehbVXuydvassVVOVkce+OvmMIjvDJtXJozx//xBiEJvd268pd/8ylbqis4/Nk67KX5gHJrsvs6tkvJMmrgcLIXXEmfmevdFbq1K2+jLAqbOZRul97tVSilwqIxWSxe1yB3w8OYQsKxlxViiopzTz4fWXkniZfd5VOGuHdSN5ksbSaNkd4WgpsWn4xVSkUDbwH3aK2PK6X8bupjXZ27iVJqMkZohz59+gQ6jFalKRN0nvF316Ri0rg5Rr76rnVMmDABU1gEDoem4L2nsJUcwxTRDW2rRtdU4NAOVFg0jqoyn+Gd4/94A2UJdTfRDu87yCumDWC3FqEsFneMHnDGzA3NmZDE3vw+/xC5YZHsA949fSjWrB3g0IZmTuQJzRzXxGvBe09hKz6KJa6728gD7r6stTV0TGFROKqsHHc4TmTHfL/f6M+qwGKGBGexlmt8KRlzKNz4KA6TIiE6AseOZRw+dgTt0H47amUfP4bQPDz/ZuFEam9L9MgVgpOACqaUUiEYRj5Ta73eufqYUqqH8/MeQK5zfQ6Q5rF7b+BI7WNqrVdorQdrrQcnJyc3dfwtir8JOkt4lN/4sGf83WWA3bnuzmrQ5Iy5mCOiiRs6gaQrZmIKCSPl6rn0mbmBlIw5RpWrOdSv9G70mSPRdpu7wKl2TLto5yqfjbkNBco8QvIP8SiKyZ+8DEDhtuUUfrSSpCvuJeGSO7FXWcnfssQdrzZHxeOorsAcmwra4RYLq8zei73C6DdbtHP1Ca360EjC0s6gW3wScEKK2OGwU209jnY4sHnMIbgI6z0QW6UVh91O3tGfyD1yGIfdjgoJ9/17iE2VydIWoDHS20LnIJCsGwW8AHyjtfasTtkITHS+n4gRu3etv/n/t3fu4VFVVx9+91yTmYTcg0BIwApobKlS+1WkBbRIAQFN1SqgqFURrdYLl9ZqrbVaP7mIVEWq1hsitVaxgIBgtUrRz7Zai0oVaJUEEXIj92Qyl/39cc4cZphJCJDJhLDe55knZ3ZmzlmZOVlnn7XX+i0z++Z0oFZr/WUn2pww4i3QVa5bTOrXJ7TZ+zXy4hB2wPGySHIn3EztO8/H/V3epDkopSxZgIaPXrf03EMtjbj6DCZ14KmEfM2Ur7wX5XRbx2zc+ibB2nKc2dFZMo1b36Rm0zLyz/85ubNfZuyArzO94jMjHPTxG5YUQtpXzyJnzDXogJ/yF++idEEJlWsfMHrKBnykfuWb+xeMNy5F+5oINdfTsOVVss+eaV2sfLs/pb62ts3P9sCLaOPWN9n9+LXokCa/b3/yjutnLYCneVNjqm4r1y4i1Fwvi6WdgGQcHXscNEavlPo2sAn4EAiZwz8D3gX+ABQCpcCFWutq88LwEDAOaAKuaC8+D90nRg9G/PKKGTPxNzfgzOlPxvCL8BaParf364G9Xfc+f3v8PqQLvw/QZo9S7C4IBbGlpkV3b1o1z9CzyehNqLmOtKFjra5I1RuXooN+PCeNjMpr3/34tfxswKl4MvJ45PQLASPmX//earS/uY2uUyUUzV1tjYUFzPpeucR6vvePv0TZbHHbE5a/eBeh1uY2P9fw5xQpeBaZW5/5nUtxpOdS+8p8gqEQIeUg2FCNcroBzcyrrzpoUxLh4EiMvucg6pVHQEd6vx7YEk+HQlSWf4nDmwUOd5uLicruJHXwcJq3v2NUlJoNuevfWw3muke4enV/Y48yszfsfgdr/a6yzJIk9hSPtlryoTUrTxqJIxTihnPnopXNuqDYe+WRO+GmuAu/IV8TzpwCMoZfhGfICOMCpJShftlQjc3tIdRU02ZVr9Yh2sL6zNpQogxfVFp2biH4xkOkpaeL7HCCEFnnnoGoVx4BB7u1Dc+IwoJktlHX4QvBs8ue5amlD5LpVlY8PTIME2yuw19VRsOWDWSPmUnhrJfIHjOThi0bAIU9tZcVaw9nv2SPmUnOhJuxe3pFKTh6i0fR98ol2HvlWfn2xsWjjLRevVEuDz/62tncOHkOWtmsUAl2ByF/S1RMPpxnn3fezyybat56hprNK3BkHkfhrJfIGXcDym4nbehYbG5v3M+nV3Zuu59rOHZP0Bc3Ruyv2mVtV1Xs4bPtn7DsmWUAXDr9UhEe60SsdZRgkM+2fyJOvocjjj4OByumiVfp6vnu9VwxYyYAFXu+IDvdYyxavvGEtSibX3Ibyu2x4uORMXp0kEDtXivWHhnLD0v+hqtVw71ed943iZC5kBqWJF5w8pm8Xl9B9nEnsOeV+2ks+9jQiX/zKXLG3YDdm0X+uT/Fc8K3qHj515QuKKH+vdWkDR0bVbzlzB9I/XurCdTsYddDl7D3+dsgFKL+g/WknXpOTNFWzbr7WfKbBzr0+R6s52v4onrgBTVS4VMQhI4jWjdxaKv3a3i8rTRMf3ODpYBYVbEHR5aRux5s3MeXT/3YmLHq+KmD2u/DkXkcjuy+RpeoppoYyd+M4RdR8af7rE5QlWsfIHfCTTRte5uKl39NqKWRNx0uUkKautpyy3kHaiusUEmwvpJAfSXN//k7eef9DHdBMaULSqyYvyUwtmUD6d+YFDUejqW7cgtxjZy+P7XSlcozv3usw7PCeO0ZK1bNQ9kc7HtrGXrHJhYumi9pgILQSciMvg3au7WNNyOt2bwCm9tLfeWXXDFjJmlpGfiryoyFRzMEUzjrJZTbE3c2q9wego21+HZ/GhMeiZQTUK4Uq6FHsK7CcNo7/saIM6+kcPZK/nbBL/ixpxf+2r1kjphC3yuXoAP7QyXOnAJqN6+IyvyxpXit7lLK7qB5+zvkTZpD8/Z3osYjs4fCoaPCWSsJ+Zq5/c67OiwbEdbnD725hNIFJVStf5CsM39I7sRbaPpwI5dcWMK0aVMlDVAQOglx9IfBgaGd6Bj3SrIn30pTEOxp2TFOVfuaYsIelesWm2qP6eRNmkPWyEvJPvtaqtYtZt9bywi1NFkx/2BdhdHQ4y9Potweajev4M4Bp7Bh4yMMrN1rhIImz426oESKnGUMvyiqQQhgKVWG8VeVWTHz9mLpYF7gvBmHHF6ZNm0qXq+X3hffQ79rHiPtq2eRUjSUnImzWbfhNUDSAAWhsxBHfxiEZ6TVq+6ldGEJDf98JSbunjtpDigV41Sduf3xFo+24uGVr9wPwQBAVJMOb/Eoown3lg3kTryFrDN/aGTtOIzCqlBLI+nDJhKo2cMfvz2N/x11OZ9n9QX2SxKHLw7h1oItO7fgGTICe1p2lAM9UKkyfDcRTwUzXLgUvkjVv7/aqsg9VOXJg83YRXhMEDoHcfSHybRpU3ny0aWk5/aJmRGD4bCCDdUxvVkzhl9E48evm9k0N4FS5E6cReHslVGKjgAtpVuiCpv6XfMY6aedS8Wqedj8zczolYejVx5fVn/BU6dNttIzw7r2Ouin/MVfUfXKIoL11VZrwWBLQ1QbwdRBw6Mkk0MtjUah2KDhMXcfFavmEWiopnRhiZHD306f14NxsBl7vBaMkustCIeOOPp2OJhkcdgROVPT2swiyRo5PUru1+7NIuT3Ubl6AdUblkT1U838ziVRaY/hEEokmSOmEGqq5XyHi/mvPkTJSSNj5ISr1i0m8zuXGLrwNhupg76FcqVg92QYOfFp2eD3GZWwC79P8/Z3cOUNsLJwlCsVb/Fomre/Y/SWffnXlC40es+GfM30vuAXFM1dTd+rlrSpW9+R8EpHZuyJSgOUfrHCsYRk3bRBZPVg9pD9AmU3z/kJi+bfx7RpU62iE39zA1VrFpAzcXaMcqQOBQn5fex94Rcomx3t96FcqbgKimne/m6UI/cWj0KHgpS/eJfxOvd+IbMwvl1bUa4UXtCKvakpfDJwGBm5hZYImT0jnyxThEwHA+jWJpr/+0/s3l7kjLthf/bMKwsJNTUQ1ptL+9oYvBf9ii9+ezWek0bS+PHrMZWrIb8PQtGaOhnDL6Jy3eKozJyKVfPITvewfPlz7Trmg2U3JQrpFysca0hlbBuEJYuDjfti5Hib/vwQl1xYwpPLniNgT4lRpHTm9CelcCj1/9qIzZ1K2te/F5OmWLF6PkrZyJ04K6Yvqw76yRp9BVUblqLsdksOgZ3/4raVv+buUIiyUABsDpTDgW5tQbk9pA+biCu3MGpfwcZ9AHH7tlatf5C+Vz1iOPJ1i/EWj6b1ow0ohwvniaNp/PgNgnUVhgSBzY6yO9H+lph9WdIKrc04Mo8jY8QUHOm53basXvrFCj0FkUA4QsIyCG0146586VeQkhYz6w021uDM6mN0aFr/IPnn30H1a0vj7+OV+wm1+rC5U2L248wuoLXic9KGjrVkDYodLjb5fdx2+g94IaeAmk3L8J58FvUfrEcphQ74saV48J58lvGeqjKUKxXd2kzh7PjaNs6c/vsvME01PP3E4wAx8g5VFXsoOn4Q48eO4akVf6TX9yJy61fPx+NUeMbNPiqcZ0ckLgThaEAkEI6Q8EJhWymGIa2j4uvhHHNls+OvKqNqwxKrL2pb+wjWV4EOxt2Pb/enVqpl5vAf4OiVzzZvNmeU3M66UdOtatmskZeSM2YGdk8v0EG8J59F09a/kDp4OPaMfPK/f3tUr9gwRgjIY+X354y7Ae1wA/vj4sueWYbX67Wc/N133sGIM85AB6J7wDptUF+776jJeZe0TeFYQxx9G4QXCu3erLjFUZHNrcOEK1xBoexOq5F3W2mKypXaZu/VcDaL19fEi+sf5NoTv0Ogdi/NXzEu3pEXj3Dxkg600rztHXLG3xhV7KQ1sY3IV88npfBr0VIMk+daaZHX/eh6Lp95Q0x+/E2z5pBxzhz6XfMYRXNX0e+ax8g4Z06bC9Ld0XlK2qZwrCGOvg2mTZvKJReWoP2+GAGwxi0bYlIhwXBsNk8Gdm82AOnfmNR2muLq+ejW5jYFwsIXiYDNTn3Ahz9/YNQFI97Fw5HRG391bLGT3dMrRssmbehYAtXR/WDcBcV8/p9t5PftzyNLloDDbXSvisiPr6qOP3MPNDceNc5T0jaFYw3JummHdRteI6/kZwQb95m6LrtQrlTyS24j2LiPqnWLrUXams0rqPv7y9hcqSiHk9xxt5BSNNRaHA3WllP+0q+MhVNXCjoQQLlSrJz1KD2ZdYvJbG2ibtU8mDyX87L7k+3NMuL+5jHDRVCRsf1gc13MXURK0VCCdRVkjphC1shLrb9NBwPU/d8fov7ems0rcHizsI26jsKIfrFg3DUYdywtcTOBwv1xuzqD5nCZNm1qt7VNEDobcfRtsHz5c3y+YxuF5xXT9Olma1z7jPTC8EJe9WtL8VeWYfNk4EjLJmfcDex9/vaYWS9KgdbknHMz/uovaNiygVBjDcrtwZU/0BIls6V48RYU8+e6cspS0rhg41L81buoWD2PvElzyfj2NCuVUqX2onLdYoJ1FTizC9C+JpwpHiu1M3wBcWYXxHXOyuWhZecW60JR//5q8ktujxIRyxl/I9WvLcVbPArfrq3Y07KjLnC+XVupWrOAp5Y+KM5TELopknUTh+XLn+Oqa6/H19pK+rCJMZ2bDmwq8sVvr7YcfOGs/Zk68VIzq9YtRoeC5J5zC9WvLQWHi2B9FXmT5kSlXl5pd1KGZn19Fc6cAhxZfWkp/RDd2oxypZJS+DVa9+wg1NJodJ9KyybL6+bC80t4ZOmjoBTKZjPWDOwObG5vVNeqqnWLSf3KN80etGXYUzwEW5rayM75Pr0vupuKVfPIOvOHKJvdSuF0Zhfgry5Dh9puOCIIQmKQrJsj4PY77yJgTyF92ETq318TJUp2YPVqy84tlp5NOFwSDrHUbHo2pj9szvgbCZmNsjOGX0Rg35eWzMFxTTUMS0kjbehYfhf0888JN1uNQFrLP0P7miiau4q0k8+kpfRDUIr8839O4eyV5E6cRW2Tj8efeArlTsXuzSD//DsonL2S3hf+0ijEMiUQyl/8FToUxN3vJLLPnonTk4b31IltK2s6XJSvvAcdDOJIz7UWf4vmriL77JnkHddPqkwFoRsjM/o42Gx2NEZv19KFJTFt8xo+ep1qM31SuT3YnClW4VN4Bh+or6TqlUXWDHl/W8BdKIeL9NPOJWvkpeycN8na/7O/v42imj2caHeRPvbauD1ZHRn5hHxNKLuTnHE3xBRbBRqqsaekkTtxVuz7V95Dfslt0fn6OoCvoRZHdgGpg4fT8MF6bG4Pgdq9RsFVUx02dypZo6+gtbKUpg83RlUA1726GB1oJeOc/Xck3bVQShB6GjKjPwIcqV4cGb3NRc1YLRdHei7Y7PS++B5srlSCviYqVs/H7s2yYuhVryxCuVOtjlCRmvT5599Bw5YN7HtrmdVRCuDWcTdw/eS5NO2Ln3evA61kj5mJDgYI1O6J0brPGXcDymY01I6fstkUk6+fnual6CuD8FeX4czuh3K6jI5Y5v5s7hQyR07H7s1C79jE1dOnRGWreF12Ms6JVu7sqHqlIAhdgzj6OPibGwjUVVL+0t34K8sof+ludt43id2PX8e+t5YZs1hzUTZYX4XdDLdUb1xK1dpFBJtrwe5AB/xUrl0UN4STN2kO9e+voaiqlKkv/YqWnVsoTc/lXb8P5YofQnHmFOzXm3d5YrTuU4qGYvf0ajP105ndP2rMXVBM5d7d3H3nHdhNbfuY4q1zZlG94RErBXHJww9FiYxVVeyJe1H5/D/bJJwjCN0EybqJQ3p6Jo1BSBs6No5GzTxCjbUoV4rRdCPFS+45hnMMpy+GdWQCNXvI/M6lVL2yKP4M29fEzNR0pjfXs/zFuygN+FAONxplpU4G6iup3bzCEixr3PomniEj0L4mAr6mmP0GaveSM+GmmMyYilXzSPv696JeGy5omjZtKpvffptHliyJaydBnyVjEBZy2/lfI4Uyt3ffmIyecJpm82mXiWiYIHQDZEYfQVi6tqGlpc1WenmT5uLM6U/+939upEi2xNeiD9TuNXrApueinLESBDWbV2DzZLBw0k849+pHUeffgT09F7Qm3ZtKsLGWvS/8Iqq5eO74G6l56xmzbWEqdjM0FIkjozeO9FwyzZ6uYZkCrUM0bf1LVOFX+cq72fmf7QwcdCIjzjiDvD792q1ujdesu76hkbpXo4vBGv+5hpyJsyWcIwjdBHH0JpFOTLe2tN9Kr3qXFX4JFyhFEg6zZIyYYjS9drqjMnW+8sF6Xvi/Fxj0vetxDTyF3dl9rZi5zeGgbl8VOuBjwMDjyZs8NyZrp/79NaQNm0RWZmZMNaoj2ELdq4uxe7Poc/lv6H3R3RDwkX7K+P3Of0EJDVs2kF9yO/1n7Zc3uKDk3HarWyObdYftyThnDl6XPSpuH/IdfjMSQRA6H3H0JpFOzJbSfis9Z04BsF+TJrJbU7jxR8bwi/BXf0GotZmQr5FQS5MlBOb663MM0CFyzf2EcRcUE2xpsp631WpPtzaROWIKVRV7Ykr5H3/kIR578P6osaunT0Hv2GQ5f0fmcTGtDz3fvZ51G15rVxqgLXuqKvZExe2LviKiYYLQnZD0SpNI6drqjUtp/HRz3Bh95dpFoDXBhmocGb0JtTYDoJxugrXllh57uPo1XAhVs3kFofdW0dDagiPzOOzBAJlmbD9My84tVK+6l9bGOgDy+/bHNuq62NeYsseHIgEcGVvXIR23MOpgMr0d1XGPbOwhKZeCkDgkvfIQiZSuzT57Jt4hI6h/f42pUWMWGr10NyG/j9xzbrHSD1HgGXwGBTN/R+6k2SiHk6q1D1D/3qqoWfOoQd/ic6U425tl9H4dfXlMC8CKVfO46vLpgOEs6xsaY4qzwiJphyoYFtmSb8AJg6Nm3I1b32T349eiQ7rdDJmOqj6KaJggdC9kRm8SbxZasXoeOuC3ioy+WHpl3EKkqvUP0u+ax6LG9v7+tqhZc6+WBu5e/xAzP92M6yerAcPB1r79PP6qMhyZx+H0N9LUUAtEd7gyCqLKUC4P2tfEgBMGc/eddxy244z8WwP1ldRsWhYljtbe7PvArJsjsUMQhCOj0zpMKaWeACYC5Vrrr5pj2cDzwADgc+AHWut9SikFLAYmAE3A5Vrr9w9mRHdw9BDrxMaPHcOzzz5HQ0sLurUFIL4WzIISel98T5SjTHHYsI26jmEpaXySV0TIZm/zolC1/kGcKsRjD95vOc1Ed0Gy/tadpeSf//OjojOUIAjRdGbo5ilg3AFjPwX+rLUeBPzZfA4wHhhkPmYAj3TU4O5AZHjjs+2fsOThh6irrWbmVT/E6UlDOd1xFxntKR6CbzwUFaZYNP8+em94gJeeuYUfbf69EXZZu4iQrykmXJPpVlFOHhLfBSn8txKM30BFMmQEoedw0IIprfVbSqkBBwyfC4w2t58G/gL8xBx/Rhu3Cf+nlMpUSvXRWn/ZWQZ3Ndf96Hoeffo5ciffSuWa+2M04CvXLcZ76kR8s4BVAQAADR5JREFUOzax7JllbH77ba6YMRN/UwPK7uRGm40X3l5BzXuGGJm730mmtn0ZypnKzKuuYMnDD8Ucd/zYMTz6xD0EfU04s/uTOng4escmFi6af8R/U+Sdi8PMMIrRl5cMGUHoMRxuZWzvsPPWWn+plMo3x/sBZRGv22WOHbWO/vGnniF38q1GA4/GanIm3GRox/saceb0J2vkdLzFo2gp+jrX/fgmGn0BLh02mQ8dbj54fzV/mnAz6QXFuMyMHVefwWSPmUnF6vm4+w5h3YbXYo65fPlzPPvCSnLP2y9AVrVmAVdPn3LE8fDI+Hz/84xsoMrV88mdFC1K1hkXFEEQugedLYGg4ozFXQRQSs3ACO9QWFjYyWZ0Hv6mBiu04cwpwJGeS8jXFKVoaS2qVleSkZHPfX9byWs6xC3n3xHVxCN3ws2Uv3gXyu7AWzwaV5/B7NzwCDa7PWphMzKnP/zenImzWbfh6SP+ew7cd1i2oXrVvQRaGq3OUGAsCMuiqyAc/RxueuVepVQfAPNnuTm+C4hUzioAdhMHrfWjWuvTtNan5eXlHaYZicfp2d/0OqwzH1a2BPYrU549k8LZK0kZfyNnKRtX+1vaVKDsf+Pvcfc7iZpNy8g//+dRzbeXL3+uzcKkzoibx9t35ogpBFoarbUJIEbqIGybIAhHH4fr6FcBl5nblwF/ihifrgxOB2qP5vg8wFWXT6dy9Xxadm7BM2QEnuLRBBqqrWrY2refJ2f8jfxw3xdM+3AjKUVD+TQ1ndbMPnEXUx0ZvdHBADWbno1RigzrwSRyIbYj+44ndSBaNYJw9HJQR6+UWgG8AwxRSu1SSl0J/C9wtlJqO3C2+RxgLfBfYAfwGHBdQqzuQpY8/BAzLptK9ap7KV1QQvO/1nLtjKt45tGHSf3H0/irynD3O4mzdvyNM//zd9CaQO1eMkZMiVsQlelWlC4ssbpSRRKetXe0MOlw6Mi+E3lHIQhC1yMFU0fICScMoeGbl5PR70RCSlHz6dtUbVhCfsltMd2fMt2KC88v4bFnVoDDHdN7NjJ/PZGFSQfbd0elDgRBSC4igXAEhOWKD9o04957+avbSei1B6n94hP2/XsT+958ivRhE6lcF60gmeo0nPyjTzxFzsTZZH7nkpgZf+TM+sCc/s5cCD3YvhN5RyEIQtcjjUcO4MD0w3abZhQUcNxp3+AHHi9Ln7qHUDBIvplp48ottPLlnalpPPnoUm6/8y6CZrOQcMaO8ZpdKIebZU8+3i0yW8I23H7nXez8w3YrE6c72CYIwqEjoZsDOGjYQmsoLYWiopj37H3+dgpntS1bYLPbcWQVkH32TAmLCIJwxEjo5jA56ELkvHkwdCj8978x72lLvz6c0VJ0/CBSBw+PCdlUrVkgYRFBEBKGhG4OoOj4QTS3JwkwdSr4/TBwYMx7wnn2kb1aI6tM777zDiMsVDya6o1L8VeXYXd7mPHDyyUsIghC4tBaJ/3xjW98Q3cXnn12uU7P66t7X/xrXTj7Zd374l/rXrl99Js/vlHrUOig78k55xbtyOyjQem8PgX62WeXx7x2wAlDtLLZ9IAThsT8XugY8jkKgtbAP3QHfGzSnbzuZo5e61gn8teZ1xof1caNHX6POJ7EEe9inJ7XVz5z4Zijo45eFmM7QigEa9fCxInJtkRA8vwFIYwsxh4pra0wZw6Ul4PNJk6+GyGVu4JwaIijb4utW2HJEnj11WRbIhxAopuyCEJPQxz9gYRDWaecAtu2waWXJtceIQap3BWEQ0PSKyNpaoILLoBrroFzz4V+/ZJtkRAHqdwVhENDHH0kgQDU1hoPoVszbdpUceyC0EHE0QPU10NKCvTqBW+9BXZ7si0SBEHoNCRG39oKY8bAVVcZz8XJC4LQw5AZvcsFF14Igwcn2xJBEISEcOw6+ooK2LfPcPCzZyfbGkEQhIRx7Dr6iy825Ia3bgWnM9nWCIIgJIxj19EvXgyVleLkBUHo8Rxbi7GlpfDkk8b2V78Ko0cn1RxBEISu4Nhy9PPnwy23GPF5QRCEY4Rjy9EvXAjvvAN5ecm2RBAEocvo+Y7+3/820icbGoxUyhNPTLZFgiAIXUrPd/SffGLM4r/8MtmWCIIgJIWe6+h9PuNnSYmhQjlIJGwFQTg26ZmO/v33Dcf+zjvGc48nufYIgiAkkZ7p6Pv0gZNPhr59k22JIAhC0ulZjn7bNqNxSJ8+sG4dFBUl2yJBEISkkxBHr5Qap5T6VCm1Qyn100QcI4Zt24yuUAsWdMnhBEEQjhY63dErpezAw8B4oBiYopQqbv9dncCgQfDLX8JllyX8UIIgCEcTiZjR/w+wQ2v9X611K/B74NwEHMfg1Vdh925QCubMgfz8hB1KEAThaCQRjr4fUBbxfJc51vnU1cHUqTB3bkJ2LwiC0BNIhHqlijOmY16k1AxgBkBhYeHhHalXL1i/XpqGCIIgtEMiZvS7gP4RzwuA3Qe+SGv9qNb6NK31aXlHoj3zzW9CRsbhv18QBKGHkwhH/3dgkFJqoFLKBVwMrErAcQRBEIQO0OmhG611QCl1PfAqYAee0Fp/3NnHEQRBEDpGQjpMaa3XAmsTsW9BEATh0OhZlbGCIAhCDOLoBUEQejji6AVBEHo44ugFQRB6OOLoBUEQejji6AVBEHo44ugFQRB6OOLoBUEQejji6AVBEHo44ugFQRB6OErrGAXhrjdCqQpg52G+PReo7ERzOgux69DprraJXYeG2HVoHIldRVrrg8r/dgtHfyQopf6htT4t2XYciNh16HRX28SuQ0PsOjS6wi4J3QiCIPRwxNELgiD0cHqCo3802Qa0gdh16HRX28SuQ0PsOjQSbtdRH6MXBEEQ2qcnzOgFQRCEdjiqHb1SapxS6lOl1A6l1E+7+NhPKKXKlVIfRYxlK6U2KqW2mz+zzHGllPqNaecWpdSwBNrVXyn1hlLq30qpj5VSN3YH25RSKUqpvyml/mXa9UtzfKBS6l3TrufNPsMopdzm8x3m7wckwq4I++xKqX8qpdZ0F7uUUp8rpT5USn2glPqHOdYdzrFMpdQflVKfmOfZ8GTbpZQaYn5O4UedUuqmZNtlHutm85z/SCm1wvxf6NrzS2t9VD4w+tH+BzgecAH/Aoq78PgjgWHARxFj84Cfmts/Be4ztycA6wAFnA68m0C7+gDDzO10YBtQnGzbzP2nmdtO4F3zeH8ALjbHlwLXmtvXAUvN7YuB5xP8fd4CPAesMZ8n3S7gcyD3gLHucI49DVxlbruAzO5gV4R9dmAPUJRsu4B+wGdAasR5dXlXn18J/cAT/GUOB16NeH4rcGsX2zCAaEf/KdDH3O4DfGpu/xaYEu91XWDjn4Czu5NtgAd4H/gWRqGI48DvFKO5/HBz22G+TiXIngLgz8BZwBrzn7872PU5sY4+qd8j0Mt0XKo72XWALWOBzd3BLgxHXwZkm+fLGuB7XX1+Hc2hm/AHGGaXOZZMemutvwQwf+ab40mx1bztOxVj9px028zwyAdAObAR446sRmsdiHNsyy7z97VATiLsAh4A5gIh83lON7FLAxuUUu8ppWaYY8n+Ho8HKoAnzVDX40opbzewK5KLgRXmdlLt0lp/ASwASoEvMc6X9+ji8+todvQqzlh3TSHqcluVUmnAi8BNWuu69l4aZywhtmmtg1rrUzBm0P8DnNTOsbvELqXURKBca/1e5HCy7TIZobUeBowHfqSUGtnOa7vKLgdGyPIRrfWpQCNGSCTZdhkHM2Ldk4EXDvbSOGOJOL+ygHOBgUBfwIvxfbZ17ITYdTQ7+l1A/4jnBcDuJNkSZq9Sqg+A+bPcHO9SW5VSTgwnv1xr/VJ3sg1Aa10D/AUjNpqplHLEObZll/n7DKA6AeaMACYrpT4Hfo8RvnmgG9iF1nq3+bMcWIlxcUz297gL2KW1ftd8/kcMx59su8KMB97XWu81nyfbrjHAZ1rrCq21H3gJOIMuPr+OZkf/d2CQuXrtwrhdW5Vkm1YBl5nbl2HEx8Pj082V/tOB2vDtZGejlFLA74B/a63v7y62KaXylFKZ5nYqxj/Av4E3gAvasCts7wXA69oMXHYmWutbtdYFWusBGOfQ61rracm2SynlVUqlh7cx4s4fkeTvUWu9ByhTSg0xh74LbE22XRFMYX/YJnz8ZNpVCpyulPKY/5vhz6trz69ELook+oGxcr4NI9Z7WxcfewVGzM2PcRW+EiOW9mdgu/kz23ytAh427fwQOC2Bdn0b41ZvC/CB+ZiQbNuAocA/Tbs+Au4wx48H/gbswLjddpvjKebzHebvj++C73Q0+7NukmqXefx/mY+Pw+d3sr9H81inAP8wv8uXgaxuYpcHqAIyIsa6g12/BD4xz/tlgLurzy+pjBUEQejhHM2hG0EQBKEDiKMXBEHo4YijFwRB6OGIoxcEQejhiKMXBEHo4YijFwRB6OGIoxcEQejhiKMXBEHo4fw/rQHoNJcAkwwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(price,np.matmul(X,theta), edgecolor='k')\n",
    "plt.plot(range(800),range(800),'r:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1189,
   "metadata": {},
   "outputs": [],
   "source": [
    "#kfold cross validation as before\n",
    "I = np.random.permutation(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1288,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:16: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  app.launch_new_instance()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 59.03982096, 147.09775895, -18.96157328,   0.        ,\n",
       "          0.        ],\n",
       "       [ 50.24036873, 150.64015283, -18.73203892,   0.        ,\n",
       "          0.        ],\n",
       "       [ 48.04656341, 148.65094307, -17.0982333 ,   0.        ,\n",
       "          0.        ],\n",
       "       [ 61.59599322, 145.94692718, -20.04006152,   0.        ,\n",
       "          0.        ],\n",
       "       [ 52.85148711, 151.58943082, -19.52162198,   0.        ,\n",
       "          0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ,   0.        ,\n",
       "          0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ,   0.        ,\n",
       "          0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ,   0.        ,\n",
       "          0.        ]])"
      ]
     },
     "execution_count": 1288,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[75.84013348, 74.74482079, 74.61082514, 73.32102496, 75.67753363],\n",
       "       [75.84013348, 74.74482079, 74.61082514, 73.32102496, 75.67753363]])"
      ]
     },
     "execution_count": 1288,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nfold = int(N/5)\n",
    "models,errors = np.zeros((8,5)), np.zeros((2,5))\n",
    "for k in range(1,6):\n",
    "    if k == 1:\n",
    "        Itrain = I[nfold+1:]\n",
    "        Itest = I[:nfold]\n",
    "#         X[Itrain,:].ndim\n",
    "    elif k==5:\n",
    "        Itrain = I[:4*nfold]\n",
    "        Itest = I[4*nfold+1:]\n",
    "#         X[Itrain,:].ndim\n",
    "    else: \n",
    "        Itrain = np.hstack((np.hstack(I[:(k-1) * nfold]), np.hstack(I[k*nfold+1:N])))\n",
    "        Itest = np.hstack((I[(k-1)*nfold+1], I[k*nfold]))\n",
    "#         X[Itrain,:].ndim\n",
    "    theta = npl.lstsq(X[Itrain,:], price[Itrain])[0]\n",
    "    errors[0,k-1] = rms(np.matmul(X[Itrain,:] , theta) - price[Itrain])\n",
    "    errors[1,k-1] = rms(np.matmul(X[Itrain,:] , theta) - price[Itrain])\n",
    "    models[k-1,:3] = theta\n",
    "\n",
    "models\n",
    "errors\n",
    "\n",
    "##k-fold validation bug persists as before, narrowed down to the dimension of X[Itrain,:] in the else step \n",
    "##hstacking/vstacking is causing unecessary nesting"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
